Stability of difference schemes for hyperbolic-parabolic equations

Abstract

The stable difference schemes approximately solving the nonlocal boundary value problem for hyperbolic-parabolic equationin a Hilbert space H with self-adjoint positive definite operator A are presented. The stability estimates for the solutions of the difference schemes of the mixed type boundary value problems for hyperbolic-parabolic equations are obtained. The theoretical statements for the solution of these difference schemes for hyperbolic-parabolic equation are supported by the results of numerical experiments. (~)

The hyperbolic-elliptic equation with the nonlocal condition

“…The formula will be written to solve the nonlocal boundary value problem (1). It is well known [17,20] that for smooth data of the problems (…”

“…They also play a very important role for mathematical modelling in many branches of science, engineering and industry. Theory and numerical methods of solutions of the boundary value problems endowed with the local and nonlocal boundary conditions for partial differential equations have been investigated by many researchers ( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein).…”

On the numerical solution of a diffusion equation arising in two-phase fluid flow

“…Many applied problems in fluid mechanics and mathematical biology were formulated as the mathematical model of partial differential equations (for instance, see [1]- [4]. Fluid flow inside capillaries were also considered with mathematical models [5]- [10].…”

On a nonlocal problem for mixed parabolic–hyperbolic type equation with nonsmooth line of type changing

“…Omitting huge amount of works, related to the studying mixed type equations, we only note some recent works on local and non-local boundary problems for parabolic-hyperbolic equations [6][7][8][9][10].…”