Stability and Consistency Analysis for Implicit Scheme for MHD Stokes Free Convective Fluid flow Model Equations Past an Infinite Vertical Porous Plate in a Variable Transverse Magnetic Field

This research has discussed an analysis of the stability of the implicit Scheme for solving nonlinear partial differential equations used to investigate MHD free convective flow of an incompressible fluid past an infinite vertical porous plate with joule heating in presence of a variable transverse magnetic field. The derivation of the implicit Scheme schemes has been presented. The stability and consistency properties of the implicit scheme are described. Von-Neumann method is used to analyze stability of the implicit scheme where the eigenvalue of the amplification matrices are tested and confirmed to be less than one. The scheme is confirmed to be unconditionally stable. Taylor's series expansion of every term in the scheme is done to analyze consistency of the implicit scheme developed where the original PDE (momentum equation) is recovered from the schemes suggesting that they are consistent. The scheme is found to be unconditionally stable and convergent.