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Finite Difference Schemes and Partial Differential Equations by John Strikwerda

Finite Difference Schemes and Partial Differential Equations John Strikwerda ebook
Page: 448
Publisher: SIAM: Society for Industrial and Applied Mathematics
ISBN: 0898715679, 9780898715675
Format: pdf

Mathematical models, typically a system of ordinary or partial differential equations, can provide considerable insight into the dynamics of biological systems. (12 hours) FEM for time-dependent linear problems. Numerical studies of some stochastic partial differential equations. The difficulty in the error analysis in finite element methods and general numerical approximations for a SPDE is the lack of regularity of its solution. (2 hours) Finite-element spaces. Iterative methods for sparse linear systems. Finite difference schemes for time discretization. Some main results on approximation theory. (8 hours) Introduction to the numerical solution of partial differential equations. (3 hours) FEM for elliptic linear problems. For initial investigations, it suffices to . Method to the stochastic parabolic equation with discretized color noise； Galerkin method to the stochastic wave equation with discretized white noise, and we obtain error estimates are comparable to the error estimates of finite difference schemes. Construction of the stiffness matrix. Numerical methods for stiff ODE systems. The spatial derivatives are approximated by finite differences, and the resulting set of ordinary differential equations is integrated over the 2-dimensional coronal domain using the second-order (in time) Heun's method with a fixed time step (0.1 day-1).