Solution of boundary eigenvalue problems and IBVP involving a system of PDEs using the successive linearization method

IF 2.3 4区工程技术 Q1 MATHEMATICS, APPLIED

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik Pub Date : 2023-07-20 DOI:10.1002/zamm.202200472

M. Narayana, P. Siddheshwar

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引用次数: 0

Abstract

The paper illustrates a numerical technique to solve a system of three partial differential equations that govern the problem of Rayleigh‐Bénard‐Brinkman convection in a two‐dimensional porous rectangular box. As a result of linear and weakly nonlinear stability analyses of the system a boundary eigenvalue problem (BEVP) and an initial boundary value problem (IBVP) arise. Spatial information on the periodicity of the convection cells is first used in the system of PDEs to make it possible for the successive linearization method (SLM) to be applied. The resulting much‐simplified versions of BEVP and the IVP are then solved by direct and time multi‐stepping versions of SLM, respectively. The SLM solution of the BEVP is compared with that obtained through MATLAB routine bvp4c and the multi‐stepping‐SLM solution of the IVP is validated with that of the Runge‐Kutta‐Fehlberg (RKF45) method (using MATLAB routine ode45). The present numerical technique is found to have quadratic convergence for any desired accuracy.

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用连续线性化方法求解一类偏微分方程系统的边界特征值问题和IBVP

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来源期刊

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik 数学-力学

CiteScore

3.30

自引率

8.70%

发文量

199

审稿时长

3.0 months

期刊介绍： ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.