A Fourth-order Tridiagonal Finite Difference Method for General Non-linear Two-point Boundary Value Problems with Mixed Boundary Conditions |
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Authors: | CHAWLA M M |
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Institution: |
Department of Mathematics, Indian Institute of Technology Hauz Khas, New Delhi-110029, India
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Abstract: | We present a new fourth-order finite difference method for thegeneral second-order non-linear differential equation yN = f(x,y, y') subject to mixed two-point boundary conditions. An interestingfeature of our method is that each discretization of the differentialequation at an interior grid point is based on just three evaluationsof f. We establish, under appropriate conditions, O(h4)-convergenceof the finite difference scheme. In the case of linear differentialequations, our finite difference scheme leads to tridiagonallinear systems. Numerical examples are considered to demonstratecomputationally the fourth order of the method. |
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