Implicit difference methods for quasilinear differential functional equations on the Haar pyramid
The author presents a new approach to the numerical solution of quasilinear first order partial differential equations. He proves that under natural assumptions on the given functions and on the mesh, there is a class of implicit difference schemes which are convergent. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for the given operators. A numerical experiment is illustrated by an example. Results obtained in this paper can be applied to differential-integral problems.
scientific article; zbMATH DE number 5296726
scientific article