High-accuracy Tridiagonal Finite Difference Approximations for Non-linear Two-point Boundary Value Problems |
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Authors: | CHAWLA M M |
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Affiliation: |
Department of Mathematics, Indian Institute of Technology Hauz Khas, New Delhi-29, India
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Abstract: | We discuss the construction of finite difference approximationsfor the non-linear two-point boundary value problem: y" = f(x,y), y(a)=A, y(b)=B. In the case of linear differential equations,the resulting finite difference schemes lead to tridiagonallinear systems. Approximations of orders higher than four involvederivatives of f. While several approximations of a particularorder are possible, we obtain the "simplest" of these approximationsleading to two high-accuracy methods of orders six and eight.These two methods are described and their convergence is established;numerical results are given to illustrate the order of accuracyachieved. |
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