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Numerical simulation for a nonlinear partial differential equation with variable coefficients by means of the discrete variational derivative method. (English) Zbl 1096.65086
The author presents a finite difference scheme for a nonlinear partial differential equation with variable coefficients by means of the discrete variational derivative method [cf. D. Furihata, J. Comput. Phys. 156, 181–205 (1999; Zbl 0945.65103); Numer. Math 87, 675–699 (2001; Zbl 0974.65086)]. The stability, the existence and uniqueness and the convergence rate of the proposed finite difference scheme are shown.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
34G25 Evolution inclusions
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