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A method of high-order accuracy for the numerical integration of boundary value problems

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Abstract

A finite-difference method for the integration of the linear two-point boundary value problem

$$y'' = f(x)y + g(x), y(a) = y_a , y(b) = y_b $$

is constructed. It uses values off′,f″,g′,g″ at the grid points to obtainO(h 8) global error, and allows strict global error bounds, while needing only the solution of a tridiagonal system of equations. Numerical examples are presented to demonstrate the practical usefulness of our method.

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Authors and Affiliations

  1. Computer Centre, Physics Department, The A.M.U. Aligarh, (U.P.), India

    Riaz A. Usmani

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  1. Riaz A. Usmani
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On sabbatical leave from the Department of Computer Science, University of Manitoba, Winnipeg, Canada.

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Usmani, R.A. A method of high-order accuracy for the numerical integration of boundary value problems. BIT 13, 458–469 (1973). https://doi.org/10.1007/BF01933410

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  • DOI: https://doi.org/10.1007/BF01933410

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