Solution of boundary eigenvalue problems and IBVP involving a system of PDEs using the successive linearization method
The paper illustrates a numerical technique to solve a system of three partial differential equationsthat govern the problem of Rayleigh-Bard-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 desiredaccuracy. 2023 Wiley-VCH GmbH.
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, Vol-103, No. 12
https://doi.org/10.1002/zamm.202200472 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85165435748&doi=10.1002%2fzamm.202200472&partnerID=40&md5=0bef6bd24d24846fbb6ef4963e3ec479
Narayana M., Department of Mathematics, The University of the West Indies, Kingston, Jamaica; Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bengaluru, India