Discrete variable methods for a boundary value problem with engineering applications

Usmani, Riaz A.

doi:10.1090/S0025-5718-1978-0483496-5

Discrete variable methods for a boundary value problem with engineering applications
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Math. Comp. 32 (1978), 1087-1096 Request permission

Abstract:

In this paper we develop numerical techniques of order 2, 4 and 6 for the solution of a fourth order linear equation. A priori error bound is obtained for the fourth order method to prove the convergence of the finite difference scheme. A sufficient condition guaranteeing the uniqueness of the solution of the boundary value problem is also given. Numerical illustrations are tabulated and results compared with the classical Runge-Kutta method.

References

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Ordinary Differential Equations with Applications

Riaz A. Usmani and Dereck S. Meek, On the application of a five-band matrix in the numerical solution of a boundary value problem, Utilitas Math. 14 (1978), 21–29. MR 511511