<p>Boundaries of stability domains for GJRKMs for the non-autonomous equation for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and cRKM for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>Boundaries of stability domains for TDRKMs with <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>Boundaries of stability domains for TDRKMs with <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> and cRKM with <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>Boundaries of stability domains for ThDRKMs at <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and classical RKM at <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>Boundaries of stability domains for ThDRKMs at <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and classical RKM at <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>7</mn> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>Stability domains of fourth-order methods.</p> Full article ">Figure 7
<p>Spectrum of matrix <math display="inline"><semantics> <mi mathvariant="bold">B</mi> </semantics></math>, corresponding to sixth-order approximations of the second derivative.</p> Full article ">Figure 8
<p>Spectrum of Jacobian matrix, corresponding to high-order approximations of the second derivative: (<b>a</b>) fourth-order approximation; (<b>b</b>) fifth-order approximation; (<b>c</b>) sixth-order approximation.</p> Full article ">Figure 9
<p>Plots of the logarithms of the absolute values of local error differences: (<b>a</b>) GJRKMs; (<b>b</b>) TDRKMs, <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>; (<b>c</b>) TDRKMs, <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <span class="html-italic">R</span> corresponds to method from [<a href="#B33-algorithms-17-00535" class="html-bibr">33</a>]; (<b>d</b>) ThDRKMs, <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <span class="html-italic">R</span> corresponds to method from [<a href="#B28-algorithms-17-00535" class="html-bibr">28</a>]; (<b>e</b>) ThDRKMs, <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <span class="html-italic">R</span> corresponds to method from [<a href="#B28-algorithms-17-00535" class="html-bibr">28</a>].</p> Full article ">Figure 10
<p>Work-precision plots for fourth-order GJRKM, applied to the problem for the Lorenz system.</p> Full article ">Figure 11
<p>The spectrum of the Jacobian matrix for the case of the system of discrete kinetic equations.</p> Full article ">Figure 12
<p>Plots of the logarithm of the practical estimations of local errors for GJRKMs.</p> Full article ">Figure 13
<p>Work-precision plots for fourth-order GJRKM, applied to the problem for the system of kinetic equations.</p> Full article ">