International Journal of Computer Mathematics, Volume 95

Volume 95, Number 1, 2018

Recent Trends in Highly Accurate and Structure-Preserving Numerical Methods for Partial Differential Equations
Preface

• 
  Qin Sheng, Yifa Tang, Bruce A. Wade, Yushun Wang:
  Recent trends in highly accurate and structure-preserving numerical methods for partial differential equations. 1-2

Original Articles

• 
  Jorge Eduardo Macías-Díaz:
  A modified exponential method that preserves structural properties of the solutions of the Burgers-Huxley equation. 3-19
• 
  Hsueh-Chen Lee:
  Adaptive weights for mass conservation in a least-squares finite element method. 20-35
• 
  Jialing Wang, Yushun Wang, Dong Liang:
  Analysis of a Fourier pseudo-spectral conservative scheme for the Klein-Gordon-Schrödinger equation. 36-60
• 
  Zhenguo Mu, Haochen Li, Yushun Wang:
  A novel energy-preserving scheme for the coupled nonlinear Schrödinger equations. 61-81
• 
  Santosh Kumar, Paramjeet Singh:
  High-order IMEX-WENO finite volume approximation for nonlinear age-structured population model. 82-97
• 
  Yufeng Xu:
  Quenching phenomenon in a fractional diffusion equation and its numerical simulation. 98-113
• 
  Wenjun Cai, Yajuan Sun, Yushun Wang, Huai Zhang:
  Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs. 114-143

Review

• 
  Hong-Lin Liao, Pin Lyu, Seakweng Vong:
  Second-order BDF time approximation for Riesz space-fractional diffusion equations. 144-158

Original Articles

• 
  Julius Osato Ehigie, Manman Zou, Xilin Hou, Xiong You:
  On modified TDRKN methods for second-order systems of differential equations. 159-173
• 
  Lizhen Chen, Gérard Labrosse:
  Temporal dynamics of the march-in-time toward the steady solution of advection-diffusion systems. 174-186
• 
  Yang Kuang, Guanghui Hu:
  An adaptive FEM with ITP approach for steady Schrödinger equation. 187-201
• 
  Sadia Arshad, Weiping Bu, Jianfei Huang, Yifa Tang, Yue Zhao:
  Finite difference method for time-space linear and nonlinear fractional diffusion equations. 202-217
• 
  Y. D. Zhang, Yanmin Zhao, Fenling Wang, Yifa Tang:
  High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes. 218-230
• 
  Jingjun Zhao, Yu Li, Yang Xu:
  Multiderivative extended Runge-Kutta-Nyström methods for multi-frequency oscillatory systems. 231-254
• 
  Cui-Cui Ji, Rui Du, Zhi-Zhong Sun:
  Stability and convergence of difference schemes for multi-dimensional parabolic equations with variable coefficients and mixed derivatives. 255-277

Volume 95, Number 2, 2018

Review

• 
  Xuanxuan Zhou, Luming Zhang:
  A conservative compact difference scheme for the Zakharov equations in one space dimension. 279-302

Original Articles

• 
  Duanmei Zhou, Jiu Ding:
  Solving the Yang-Baxter-like matrix equation for nilpotent matrices of index three. 303-315
• 
  Xinrong Cong, Longsuo Li:
  Analysis on the stability of numerical schemes for a class of stochastic partial differential systems. 316-328
• 
  Jianchao Bai, Jicheng Li, Junkai Deng:
  A class of multilevel structured low-rank approximation arising in material processing. 329-340
• 
  Jingtang Ma, Hongji Tang, Song-Ping Zhu:
  Connection between trinomial trees and finite difference methods for option pricing with state-dependent switching rates. 341-360
• 
  Rui Li, Jie Chen, Zhangxin Chen, Yali Gao:
  A decoupled scheme with leap-frog multi-time step for non-stationary Stokes-Darcy system. 361-381
• 
  Xiangrong Li, Xiaoliang Wang, Zhou Sheng, Xiabin Duan:
  A modified conjugate gradient algorithm with backtracking line search technique for large-scale nonlinear equations. 382-395
• 
  Zhengguang Liu, Aijie Cheng, Xiaoli Li:
  A second-order finite difference scheme for quasilinear time fractional parabolic equation based on new fractional derivative. 396-411
• 
  Qin Gao, Quanting Zhao, Minhong Chen:
  On a modified Numerov's method for inverse Sturm-Liouville problems. 412-426
• 
  Fatemeh Panjeh Ali Beik, Salman Ahmadi-Asl, Arezo Ameri:
  On the iterative refinement of the solution of ill-conditioned linear system of equations. 427-443
• 
  Z. van der Have, Cornelis W. Oosterlee:
  The COS method for option valuation under the SABR dynamics. 444-464

Volume 95, Number 3, 2018

Review

• 
  Payel Das, Gnaneshwar Nelakanti, Guangqing Long:
  Discrete Legendre spectral Galerkin method for Urysohn integral equations. 465-489

Original Articles

• 
  Abhishek Das, Srinivasan Natesan:
  Second-order uniformly convergent numerical method for singularly perturbed delay parabolic partial differential equations. 490-510
• 
  Weisheng Zhao, Heping Zhang:
  Upper bounds on the bondage number of the strong product of a graph and a tree. 511-527
• 
  Fariba Rostami, Ahmad Jafarian:
  A new artificial neural network structure for solving high-order linear fractional differential equations. 528-539
• 
  Rongjun Cheng, Feng-Xin Sun, Jufeng Wang:
  Meshless analysis of two-dimensional two-sided space-fractional wave equation based on improved moving least-squares approximation. 540-560
• 
  Dang Van Hieu:
  Two hybrid algorithms for solving split equilibrium problems. 561-583
• 
  M. H. Rashid:
  Convergence analysis of a variant of Newton-type method for generalized equations. 584-600
• 
  R. C. Mittal, Sapna Pandit:
  Sensitivity analysis of shock wave Burgers' equation via a novel algorithm based on scale-3 Haar wavelets. 601-625
• 
  Bartosz Andreatto, Aleksandr Cariow:
  Automatic generation of fast algorithms for matrix-vector multiplication. 626-644

Volume 95, Number 4, 2018

Review

• 
  Mostafa Zahri:
  Barycentric interpolation of interface solution for solving stochastic partial differential equations on non-overlapping subdomains with additive multi-noises. 645-685

Original Articles

• 
  Yun-Bo Yang, Yao-Lin Jiang:
  Analysis of two decoupled time-stepping finite-element methods for incompressible fluids with microstructure. 686-709
• 
  Haifeng Ma:
  Acute perturbation bounds of weighted Moore-Penrose inverse. 710-720
• 
  Mojtaba Nouri Bygi, Mohammad Ghodsi:
  Weak visibility queries of line segments in simple polygons and polygonal domains. 721-738
• 
  Li Dong, Jingyong Tang, Xinyu Song:
  A non-monotone inexact non-interior continuation method based on a parametric smoothing function for LWCP. 739-751
• 
  H. S. Shukla, Mohammad Tamsir, Ram Jiwari, Vineet K. Srivastava:
  A numerical algorithm for computation modelling of 3D nonlinear wave equations based on exponential modified cubic B-spline differential quadrature method. 752-766
• 
  Khosro Sayevand, K. Pichaghchi:
  A novel operational matrix method for solving singularly perturbed boundary value problems of fractional multi-order. 767-796
• 
  Kai Cao, Daniel Lesnic:
  Reconstruction of the perfusion coefficient from temperature measurements using the conjugate gradient method. 797-814
• 
  Mahboub Baccouch:
  A posteriori local discontinuous Galerkin error estimates for the one-dimensional sine-Gordon equation. 815-844

Volume 95, Number 5, 2018

Review

• 
  Huali Zhao, Hongwei Liu:
  Infeasible path-following interior point algorithm for Cartesian P*(κ) nonlinear complementarity problems over symmetric cones. 845-869
• 
  Maziar Raissi, Padmanabhan Seshaiyer:
  Application of local improvements to reduced-order models to sampling methods for nonlinear PDEs with noise. 870-880
• 
  Salima Kouser, Shafiq ur Réhman, Fayyaz Ahmad, Stefano Serra-Capizzano, Malik Zaka Ullah, Ali Saleh Alshomrani, Hani M. Aljahdali, Shamshad Ahmad, Shahid Ahmad:
  Generalized newton multi-step iterative methods GMNp, m for solving system of nonlinear equations. 881-897

Original Articles

• 
  Sirilak Sriburadet, Bor-Wen Jeng, Cheng-Sheng Chien:
  Efficient continuation methods for spin-1 Bose-Einstein condensates in a magnetic field. 898-919
• 
  Janak Raj Sharma, Himani Arora:
  Efficient higher order derivative-free multipoint methods with and without memory for systems of nonlinear equations. 920-938
• 
  Yu Xiao, Mahmoud A. Eissa, Boping Tian:
  Convergence and stability of split-step theta methods with variable step-size for stochastic pantograph differential equations. 939-960
• 
  Feng Liao, Luming Zhang:
  Numerical analysis of a conservative linear compact difference scheme for the coupled Schrödinger-Boussinesq equations. 961-978
• 
  Jiyong Li, Ming Lu, Xuli Qi:
  Trigonometrically fitted multi-step hybrid methods for oscillatory special second-order initial value problems. 979-997
• 
  Xiaoyong Xu, Da Xu:
  Legendre wavelets method for approximate solution of fractional-order differential equations under multi-point boundary conditions. 998-1014
• 
  Qing Xue, Jing Niu, Dandan Yu, Cuiping Ran:
  An improved reproducing kernel method for Fredholm integro-differential type two-point boundary value problems. 1015-1023
• 
  Siraj-ul-Islam, Sakhi Zaman:
  Numerical methods for multivariate highly oscillatory integrals. 1024-1046

Volume 95, Numbers 6-7, 2018

Advances on Computational Fractional Partial Differential Equations
Preface

• 
  Khaled M. Furati, Abdul Q. M. Khaliq, Changpin Li, Mohsen Zayernouri:
  Preface. 1047

Reviews

• 
  Changpin Li, An Chen:
  Numerical methods for fractional partial differential equations. 1048-1099

Original Articles

• 
  Zivorad Tomovski, Trifce Sandev:
  Distributed-order wave equations with composite time fractional derivative. 1100-1113
• 
  Ye Hu, Changpin Li, Hefeng Li:
  The finite difference method for Caputo-type parabolic equation with fractional Laplacian: more than one space dimension. 1114-1130
• 
  Bo Yu, Xiaoyun Jiang, Haitao Qi:
  Numerical method for the estimation of the fractional parameters in the fractional mobile/immobile advection-diffusion model. 1131-1150
• 
  Yanzhi Liu, Jason Roberts, Yubin Yan:
  A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes. 1151-1169
• 
  Khosro Sayevand, Mohammadreza Rostami, H. S. Attari:
  A new study on delay fractional variational problems. 1170-1194
• 
  Yufeng Xu, Hai-Wei Sun, Qin Sheng:
  On variational properties of balanced central fractional derivatives. 1195-1209
• 
  X. Y. Li, B. Y. Wu:
  Iterative reproducing kernel method for nonlinear variable-order space fractional diffusion equations. 1210-1221
• 
  A. Abirami, P. Prakash, K. Thangavel:
  Fractional diffusion equation-based image denoising model using CN-GL scheme. 1222-1239
• 
  Khaled M. Furati, Muhammad S. Yousuf, A. Q. M. Khaliq:
  Fourth-order methods for space fractional reaction-diffusion equations with non-smooth data. 1240-1256
• 
  Maryam Naghibolhosseini, Glenis R. Long:
  Fractional-order modelling and simulation of human ear. 1257-1273
• 
  Olaniyi Samuel Iyiola, E. O. Asante-Asamani, Khaled M. Furati, A. Q. M. Khaliq, Bruce A. Wade:
  Efficient time discretization scheme for nonlinear space fractional reaction-diffusion equations. 1274-1291
• 
  Hu Chen, Tao Sun:
  A Petrov-Galerkin spectral method for the linearized time fractional KdV equation. 1292-1307
• 
  Shengyue Li, Zhaojie Zhou:
  Legendre pseudo-spectral method for optimal control problem governed by a time-fractional diffusion equation. 1308-1325
• 
  Sergiy Y. Reutskiy, Ji Lin:
  A semi-analytic collocation method for space fractional parabolic PDE. 1326-1339
• 
  Ehsan Kharazmi, Mohsen Zayernouri:
  Fractional pseudo-spectral methods for distributed-order fractional PDEs. 1340-1361
• 
  Angel Durán:
  An efficient method to compute solitary wave solutions of fractional Korteweg-de Vries equations. 1362-1374
• 
  Andreas Kleefeld, Sophia Vorderwülbecke, Bernhard Burgeth:
  Anomalous diffusion, dilation, and erosion in image processing. 1375-1393
• 
  Zongze Yang, Jungang Wang, Yan Li, Yufeng Nie:
  Effective numerical treatment of sub-diffusion equation with non-smooth solution. 1394-1407
• 
  Muhammad S. Yousuf:
  A second-order efficient L-stable numerical method for space fractional reaction-diffusion equations. 1408-1422
• 
  Xavier Antoine, Qinglin Tang, Jiwei Zhang:
  On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations. 1423-1443
• 
  Mohammed Alhorani, Roshdi Khalil:
  Total fractional differentials with applications to exact fractional differential equations. 1444-1452

Volume 95, Number 8, 2018

Review

• 
  Shang Liu, Yanping Chen, Yunqing Huang, Jie Zhou:
  Two-grid methods for miscible displacement problem by Galerkin methods and mixed finite-element methods. 1453-1477
• 
  Leijie Qiao, Da Xu:
  Orthogonal spline collocation scheme for the multi-term time-fractional diffusion equation. 1478-1493
• 
  Dan Li, Detong Zhu:
  An affine scaling interior trust-region method combining with nonmonotone line search filter technique for linear inequality constrained minimization. 1494-1526

Original Articles

• 
  Wei Gao, Weifan Wang:
  Analysis of k-partite ranking algorithm in area under the receiver operating characteristic curve criterion. 1527-1547
• 
  Qasem M. Al-Mdallal, Mohammed Abdalla Al-Refai, Muhammed I. Syam, Moh'd Khier Al-Srihin:
  Theoretical and computational perspectives on the eigenvalues of fourth-order fractional Sturm-Liouville problem. 1548-1564
• 
  Ricardo Crisóstomo:
  Speed and biases of Fourier-based pricing choices: a numerical analysis. 1565-1582
• 
  Jialing Wang, Yushun Wang:
  Numerical analysis of a new conservative scheme for the coupled nonlinear Schrödinger equations. 1583-1608
• 
  Yulan Wang, Mingjing Du, Temuer Chaolu, Dan Tian:
  Using reproducing kernel for solving a class of time-fractional telegraph equation with initial value conditions. 1609-1621
• 
  Tushar Chourushi:
  Computationally inexpensive and revised normalized weighting factor method for segregated solvers. 1622-1653
• 
  Mir Sajjad Hashemi, E. Darvishi, M. Inc:
  A geometric numerical integration method for solving the Volterra integro-differential equations. 1654-1665
• 
  Xifu Liu:
  Hermitian and non-negative definite reflexive and anti-reflexive solutions to AX=B. 1666-1671
• 
  Lisha Wang, Wendi Qin, Xiaohua Ding:
  Dissipativity of θ-methods for a class of advection-reaction-diffusion equations with both fixed and distributed delays. 1672-1687
• 
  Yuan Wu, Jin Liang:
  A new model and its numerical method to identify multi credit migration boundaries. 1688-1702
• 
  Ke Su, Dan Yang:
  A smooth Newton method with 3-1 piecewise NCP function for generalized nonlinear complementarity problem. 1703-1713

Volume 95, Number 9, 2018

Original Articles

• 
  Qian Guo, Wei Liu, Xuerong Mao, Weijun Zhan:
  Multi-level Monte Carlo methods with the truncated Euler-Maruyama scheme for stochastic differential equations. 1715-1726
• 
  Sean Breckling, Monika Neda:
  Numerical study of the Navier-Stokes-α deconvolution model with pointwise mass conservation. 1727-1760
• 
  Dong-Yuh Yang, Ya-Dun Chang:
  Sensitivity analysis of the machine repair problem with general repeated attempts. 1761-1774
• 
  Ranjit Kumar Upadhyay, Sangeeta Kumari:
  Bifurcation analysis of an e-epidemic model in wireless sensor network. 1775-1805
• 
  Zhongdi Cen, Aimin Xu, Anbo Le:
  A high-order finite difference scheme for a singularly perturbed fourth-order ordinary differential equation. 1806-1819
• 
  Razika Boutrig, Mustapha Chellali:
  Total vertex-edge domination. 1820-1828
• 
  Jian Lu, Ke Qiao, Lixin Shen, Yuru Zou:
  Fixed-point algorithms for a TVL1 image restoration model. 1829-1844
• 
  Zhengguang Shi, Yanmin Zhao, Yifa Tang, Fenling Wang, Yanhua Shi:
  Superconvergence analysis of an H1-Galerkin mixed finite element method for two-dimensional multi-term time fractional diffusion equations. 1845-1857
• 
  Hadi Nosratipour, Omid Solaymani Fard, Akbar Hashemi Borzabadi:
  Optimal control of viscous Burgers equation via an adaptive nonmonotone Barzilai-Borwein gradient method. 1858-1873
• 
  Feng Liao, Luming Zhang:
  Optimal error estimates of explicit finite difference schemes for the coupled Gross-Pitaevskii equations. 1874-1892
• 
  Xiaoli Feng, Zhi Qian:
  An a posteriori wavelet method for solving two kinds of ill-posed problems. 1893-1909

Review

• 
  C. Lakshmi, Ashish Awasthi:
  Robust numerical scheme for nonlinear modified Burgers equation. 1910-1926

Volume 95, Number 10, 2018

Reviews

• 
  Dongyan Li, Xingyuan Wang, Penghe Huang:
  A Max-Min ant colony algorithm for fractal dimension of complex networks. 1927-1936

Original Articles

• 
  Suheil A. Khuri, Ali Sayfy:
  Numerical solution of functional differential equations: a Green's function-based iterative approach. 1937-1949
• 
  Hamid Esmaeili, Majid Rostami, Morteza Kimiaei:
  Combining line search and trust-region methods for ℓ1-minimization. 1950-1972
• 
  Mingxu Yi, Yunpeng Ma, Lifeng Wang:
  An efficient method based on the second kind Chebyshev wavelets for solving variable-order fractional convection diffusion equations. 1973-1991
• 
  Abdolali Neamaty, Shahrbanoo Akbarpoor, Emrah Yilmaz:
  Solving inverse Sturm-Liouville problem with separated boundary conditions by using two different input data. 1992-2010
• 
  Haixiang Zhang, Xuehua Yang:
  The BDF orthogonal spline collocation method for the two-dimensional evolution equation with memory. 2011-2025
• 
  Jiandong Zhao, Lisha Wang, Zhixia Han:
  Stability analysis of two new SIRS models with two viruses. 2026-2035
• 
  Chunyan Li, Qibin Fan:
  Multiplicative noise removal via combining total variation and wavelet frame. 2036-2055
• 
  Ruyun Chen, Xuesong Kuang, Zhi Li:
  Numerical computation of infinite Bessel transforms with high frequency. 2056-2065
• 
  Mehdi Dehghan, Mansour Safarpoor:
  Application of the dual reciprocity boundary integral equation approach to solve fourth-order time-fractional partial differential equations. 2066-2081
• 
  Zhongbo Sun, Hongyang Li, Jing Wang, Yantao Tian:
  Two modified spectral conjugate gradient methods and their global convergence for unconstrained optimization. 2082-2099
• 
  Gül Gözde Biçer, Yalçin Öztürk, Mustafa Gülsu:
  Numerical approach for solving linear Fredholm integro-differential equation with piecewise intervals by Bernoulli polynomials. 2100-2111
• 
  Xiaofeng Wang:
  A family of Newton-type iterative methods using some special self-accelerating parameters. 2112-2127
• 
  Mohammadreza Foroutan, Ali Ebadian, Raheleh Asadi:
  Reproducing kernel method in Hilbert spaces for solving the linear and nonlinear four-point boundary value problems. 2128-2142

Volume 95, Number 11, 2018

Reviews

• 
  Krzysztof Gawryluk, Tomasz Karpiuk, Mariusz Gajda, Kazimierz Rzazewski, Miroslaw Brewczyk:
  Unified way for computing dynamics of Bose-Einstein condensates and degenerate Fermi gases. 2143-2161
• 
  Feifei Liu, Yulan Wang, Shuguang Li:
  Barycentric interpolation collocation method for solving the coupled viscous Burgers' equations. 2162-2173

Articles

• 
  Min Surp Rhee, Young Ik Kim, Beny Neta:
  An optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed points. 2174-2211
• 
  Yigui Ou, Xin Zhou:
  A nonmonotone scaled conjugate gradient algorithm for large-scale unconstrained optimization. 2212-2228
• 
  Zdenek Dostál, Lukás Pospísil:
  Conjugate gradients for symmetric positive semidefinite least-squares problems. 2229-2239
• 
  Shuhuang Xiang, Bin Li, Guidong Liu:
  On efficient computation of highly oscillatory retarded potential integral equations. 2240-2255
• 
  Zhenping Li, C. Xu, M. Lan, Z. Qian:
  A mollification method for a Cauchy problem for the Helmholtz equation. 2256-2268
• 
  Julio B. Clempner, Alexander S. Poznyak:
  Using the Manhattan distance for computing the multiobjective Markov chains problem. 2269-2286
• 
  Esmail Hesameddini, Mehdi Shahbazi:
  Hybrid Bernstein Block-Pulse functions for solving system of fractional integro-differential equations. 2287-2307
• 
  Shafiullah Khan, M. Kamran, Obaid Ur Rehman, Lei Liu, Shiyou Yang:
  A modified PSO algorithm with dynamic parameters for solving complex engineering design problem. 2308-2329
• 
  Mohd. Junaid Siddiqui, Rajan Arora, V. P. Singh:
  Propagation of non-linear waves in a non-ideal relaxing gas. 2330-2342
• 
  Mohan K. Kadalbajoo, Alpesh Kumar, Lok Pati Tripathi:
  Radial-basis-function-based finite difference operator splitting method for pricing American options. 2343-2359

Volume 95, Number 12, 2018

Reports

• 
  Editors' Report. 2361-2362

Original Article

• 
  Wei Zhang, M. H. Song, M. Z. Liu:
  Strong convergence of the truncated Euler-Maruyama method for stochastic functional differential equations. 2363-2387
• 
  Zepeng Li, Jin Xu:
  On the trees with same signed edge and signed star domination numbers. 2388-2395
• 
  Fakhrodin Mohammadi:
  An efficient fractional-order wavelet method for fractional Volterra integro-differential equations. 2396-2418
• 
  Chengjian Zhang, Wansheng Wang, Bochao Liu, Tingting Qin:
  A multi-domain Legendre spectral collocation method for nonlinear neutral equations with piecewise continuous argument. 2419-2432
• 
  Junying Cao, Lizhen Chen, Ziqiang Wang:
  A high-order numerical scheme for the impulsive fractional ordinary differential equations. 2433-2457
• 
  Maohua Ran, Yu He:
  Linearized Crank-Nicolson method for solving the nonlinear fractional diffusion equation with multi-delay. 2458-2470
• 
  Songqiang Qiu, Zhongwen Chen:
  A central path interior point method for nonlinear programming and its local convergence. 2471-2495
• 
  Gengen Zhang, Aiguo Xiao, Jie Zhou:
  Implicit-explicit multistep finite-element methods for nonlinear convection-diffusion-reaction equations with time delay. 2496-2510
• 
  Xiuyan Li, Chiping Zhang, Qiang Ma, Xiaohua Ding:
  Discrete gradient methods and linear projection methods for preserving a conserved quantity of stochastic differential equations. 2511-2524
• 
  Mingzhu Li, Qiang Ma, Xiaohua Ding:
  A compact ADI Crank-Nicolson difference scheme for the two-dimensional time fractional subdiffusion equation. 2525-2538
• 
  Yingxiang Xu, Li Yang:
  Optimization of a parameterized inexact Uzawa method for saddle point problems. 2539-2548
• 
  Yanying Ma, Jin Huang, Changqing Wang:
  Numerical solution of nonlinear two-dimensional Fredholm integral equations of the second kind using Sinc Nyström method. 2549-2568

Lists of Reviewers

• 
  Acknowledgement. 2569-2573