Equivalence theorem of nonlinear difference methods for initial-value problems. (Chinese. English summary) Zbl 0701.65060
The author presents the concepts of seminorm and generalized solution of an operator of the nonlinear difference approximation. By introducing new concepts of consistency, stability and convergence, the author proves the Lax equivalence theorem for the nonlinear initial value problem.
Reviewer: M.Z.Qin
MSC:
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K55 | Nonlinear parabolic equations |
| 35G10 | Initial value problems for linear higher-order PDEs |
| 35K25 | Higher-order parabolic equations |
