Numerical Solution of Stochastic Hyperbolic Equations

Abstract

A two-step difference scheme for the numerical solution of the initial-boundary value problem for stochastic hyperbolic equations is presented. The convergence estimate for the solution of the difference scheme is established. In applications, the convergence estimates for the solution of the difference scheme are obtained for different initialboundary value problems. The theoretical statements for the solution of this difference scheme are supported by numerical examples.

Second Order Equations in Functional Spaces: Qualitative and Discrete Well-Posedness

“…Section 7.5 is devoted to stochastic hyperbolic equations. It is based on results of [92,93]. Section 7.6 is devoted to fractional hyperbolic differential and difference equations.…”

A note on the numerical solution of an identification problem for observing two‐phase flow in capillaries

“…When the analytical methods do not work properly, numerical solutions of partial differential equations play a vital role in applied sciences [25][26][27][28][29][30][31]. Although there have been hundreds of such studies concerning classical partial differential equations, there has been a growing interest for numerical solutions of inverse problems (for instance, see [32][33][34][35][36][37]).…”

Difference schemes for the semilinear integral-differential equation of the hyperbolic type

“…[16,17]. There is a great deal of work in constructing and analysing difference schemes for numerical solutions of hyperbolic differential equations [1,[3][4][5][6][7][8][9][10][11][12]. In [2], linear integral-differential equations of the hyperbolic type with two dependent limits have been studied.…”