One-parameter orthogonal spline collocation methods for nonlinear two-dimensional Sobolev equations with time-variable delay

doi:10.1016/j.cnsns.2021.106233

One-parameter orthogonal spline collocation methods for nonlinear two-dimensional Sobolev equations with time-variable delay

2022-05-01

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DOI：10.1016/j.cnsns.2021.106233

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This paper deals with the numerical solutions of initial-boundary value problems (IBVPs) of nonlinear two-dimensional Sobolev equations with time-variable delay. For solving this type of IBVPs, two classes of one-parameter orthogonal spline collocation (OSC) methods are constructed. For the obtained one-parameter OSC methods, their errors in L-2- and H-1-norm are analyzed and thus the corresponding error estimates are derived. With some numerical experiments, the computational effectiveness and theoretical accuracy of the methods are further confirmed. Moreover, a numerical comparison shows that the both kinds of one-parameter OSC methods have almost the same computational efficiency and accuracy under the same parameter and stepsizes. (c) 2021 Elsevier B.V. All rights reserved.

Keywords:

Sobolev equations with time-variable delay

One-parameter orthogonal spline collocation methods

Error analysis

Numerical simulation

One-parameter orthogonal spline collocation methods for nonlinear two-dimensional Sobolev equations with time-variable delay

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