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This is a Quantitative Study study.

October 18, 2025Open Access

Spatial two-grid compact difference scheme for two-dimensional nonlinear diffusion-wave equations with variable exponent

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This analysis develops a two-grid compact difference scheme for nonlinear diffusion-wave equations, indicating stability and convergence.

The proposed scheme shows stable and convergent behavior for the two-dimensional nonlinear diffusion-wave equation.
Using a small-scale nonlinear system on the coarse grid allows efficient computations while maintaining accuracy.
Numerical experiments validate the accuracy and efficiency of the developed compact difference scheme.
This method effectively handles varying material properties in viscoelastic media through variable exponent formulations.

Zhang et al. (2025) studied this question.

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