Abstract
The second order of accuracy difference scheme generated by Crank-Nicholson difference scheme for approximately solving multipoint nonlocal boundary value problem is considered. Well-posedness of this difference scheme in Holder spaces is established. Furthermore, as applications, coercivity estimates in Holder norms for approximate solutions of the multipoint nonlocal boundary value problems for mixed type equations are obtained. Moreover, the method is illustrated by numerical examples.
Highlights
More and more mathematicians have been studying nonlocal problems for ordinary differential equations and partial differential equations because of their existence in many applied problems included in applied sciences
Several types of problems in fluid mechanics, other areas of physics, and mathematical biology led to partial differential equations of elliptic-parabolic type
The purpose of this paper is to study the second order of accuracy difference schemes of elliptic-parabolic problem with nonlocal boundary value problems
Summary
More and more mathematicians have been studying nonlocal problems for ordinary differential equations and partial differential equations because of their existence in many applied problems included in applied sciences. The purpose of this paper is to study the second order of accuracy difference schemes of elliptic-parabolic problem with nonlocal boundary value problems. The well-posedness of multipoint nonlocal boundary value problem ( ) in Hölder spaces with a weight was established. In [ ], we studied the well-posedness of the first order of accuracy difference scheme for the approximate solution of boundary value problem ( ) under assumption ( ). The well-posedness of difference scheme ( ) in Hölder spaces is established. The stability, almost coercivity stability, coercivity stability estimates for solutions of the second order of accuracy difference scheme for elliptic-parabolic equations are obtained. The theoretical statements for the solution of the first and second order of accuracy schemes for one-dimensional elliptic-parabolic differential equation are supported by the results of a numerical example
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