Applied Numerical Mathematics

This paper mainly presents numerical solutions to an initial-boundary value problem of the time-fractional Klein-Gordon equations. We developed a numerical scheme with the help of the finite difference methods and the predictor-corrector methods ...

We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which preserves the ...

This paper is dedicated to the numerical solution of a mathematical model that describes frictional quasistatic contact between an elastic body and a moving foundation, with the wear effect on the contact interface of the moving foundation due to ...

In this paper we propose a high-order spline finite element method for solving a class of time-dependent electromagnetic waves and its associated frequency-domain approach. A Fourier transform and its inverse are used for the time integration of ...

The mathematical modeling of the propagation of diseases has an important role from both mathematical and biological points of view. In this article, we observe an SEIR-type model with a general incidence rate and a non-constant recruitment rate ...

• SEIR models with general incidence and recruitment rates have a (biologically reasonable) unique solution.
• For a sufficiently small time-step, the SSP Runge-Kutta methods preserve the properties of the continuous model.
• Numerical ...

In this paper, we develop a mapped Jacobi spectral Galerkin method for solving the multi-term Fredholm integral equations (MFIEs) with two-sided weakly singularities. We introduce a new family of mapped Jacobi functions (MJFs) and establish the ...

In this paper, we study a posteriori error estimates for one-dimensional and two-dimensional linear parabolic equations. The backward Euler method and the Crank–Nicolson method for the time discretization are used, and the second-order finite ...

In this paper, we investigate properties of standard and multilevel Monte Carlo methods for weak approximation of solutions of stochastic differential equations (SDEs) driven by infinite-dimensional Wiener process and Poisson random measure with ...

In this paper, we consider a class of k-order ( 3 ≤ k ≤ 5 ) backward differentiation formulas (BDF-k) for the molecular beam epitaxial (MBE) model without slope selection. Convex splitting technique along with k-th order Douglas-Dupont ...

A BDM type of H ( div ) mixed finite element is constructed on polygonal and polyhedral meshes. The flux space is the H ( div ) subspace of the n-product Π i P k ( T i ) d space such that the divergence is a one-piece P k − 1 polynomial on the ...

In this work, we consider a more general version of the nonlocal thermistor problem, which describes the temperature diffusion produced when an electric current passes through a material. We investigate the doubly nonlinear problem where the ...

The Neumann–Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for certain ...

This article focuses on developing and analyzing an efficient higher-order numerical approximation of singularly perturbed two-dimensional semilinear parabolic convection-diffusion problems with time-dependent boundary conditions. We approximate ...

In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg–Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this aim, we ...

• Lawson and splitting methods of order 4 for Complex Ginzburg–Landau equations.
• Efficient implementation by tensor-matrix products or FFT techniques.
• Physical 2D and 3D numerical examples (cubic, cubic-quintic, and coupled CGL).

In this study, we have derived a thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects. This model accommodates variations in physical properties such as density, viscosity, heat capacity, and thermal ...

• A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects.
• A semi-decoupled, mass-preserving, and entropy-stable numerical method.
• Investigated numerically the merging process of two bubbles ...

We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the reliable cell ...

In this paper we propose an approximation method based on the classical Schoenberg-Marsden variation diminishing operator with applications to the construction of new quadrature rules. We compare the new operator with the multilevel one studied ...