Publication

Abstract : A procedure to incorporate the domain decomposition concept over the finite difference and differential quadrature methods is presented. In this procedure, three numerical schemes are formulated for solving reaction-diffusion and convection-diffusion-reaction systems. The physical domain is subdivided, and the mesh generation is done locally in each subdomain. Numerical schemes are formulated by employing suitable combinations of differential quadrature and finite difference methods for spatial and temporal derivative approximations in each subdomain. Its essence is computing the solution at the subdomain interfaces (pseudo-boundaries) first and then the solution in the subdomains by using the estimated pseudo-boundary conditions. On a two-component reaction-diffusion system, convergence, stability, the effect of grid refinement on computational time and errors are investigated. These schemes are also extended to solve the system of Black-Scholes equations for pricing European options in a regime-switching economy.