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Finite Difference Schemes and Partial Differential Equations John Strikwerda
Publisher: SIAM: Society for Industrial and Applied Mathematics

Iterative methods for sparse linear systems. Finite difference schemes for time discretization. I did a matrix rank test some time ago, and I also did finite difference scheme for pde and a direct solver using sparse matrix. In both cases, Mathematica was faster (2 times faster in the later case). This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. (2 hours) Finite-element spaces. (8 hours) Introduction to the numerical solution of partial differential equations. In the finite difference algorithm we approximated the derivatives in the PDE using standard central approximation with a Crank-Nicolson scheme, equally weighing an implicit and an explicit scheme. Construction of the stiffness matrix. (3 hours) FEM for elliptic linear problems. Some main results on approximation theory. (12 hours) FEM for time-dependent linear problems. Numerical methods for stiff ODE systems. In Physics, to simulate physical system, we usually encounter ordinary or partial differential equations. I had explored the issue of pricing a barrier using finite difference discretization of the Black-Scholes PDE a few years ago.