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Finite Difference Methods for Boundary Value Problems

Finite Difference Methods for Boundary Value ProblemsOctober 2, 2013() Finite DifferencesOctober 2, 20131 / 52 GoalsLearn steps to approximate BVPs using the Finite Difference MethodStart with two-point BVP (1D)Investigate common FD approximations foru (x) andu (x) in 1 DUse FD quotients to write a system of Difference equations to solvetwo-point BVPH igher order accurate schemesSystems of first order BVPsUse what we learned from 1D and extend to Poisson s equation in 2D& 3 DLearn how to handle different Boundary conditions() Finite DifferencesOctober 2, 20132 / 52 Steps in the Finite Difference Approach to linear DirichletBVPsOverlay domain with gridChoose Difference quotients to approximate derivatives in DEWrite a Difference equation at each node where there is an u

Finite Di erence Methods for Boundary Value Problems October 2, 2013 Finite Di erences October 2, 2013 1 / 52. Goals Learn steps to approximate BVPs using the Finite Di erence Method Start with two-point BVP (1D) Investigate common FD approximations for u0(x) and u00(x) in 1D Use FD quotients to write a system of di erence equations to solve

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