A numerical algorithm for determination of a control parameter in two-dimensional parabolic inverse problems

被引：0
作者：
Akbar Mohebbi
机构：
[1] University of Kashan,Department of Applied Mathematics, Faculty of Mathematical Science
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2015年 / 31卷
关键词：
compact finite difference scheme; boundary value method; control parameter; parabolic inverse problem; temperature over-specification; high accuracy; noise; 05C15; 60C05;
D O I：
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中图分类号：
学科分类号：
摘要：
Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown control parameter and unknown solution of two-dimensional parabolic inverse problem with overspecialization at a point in the spatial domain. In this approach, a compact fourth-order scheme is used to discretize spatial derivatives of equation and reduces the problem to a system of ordinary differential equations (ODEs). Then we apply a fourth order boundary value method to the solution of resulting system of ODEs. So the proposed method has fourth order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes in the literature. Also we will investigate the effect of noise in data on the approximate solutions.
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页码：213 / 224
页数：11
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