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On the Numerical Solution of Linear and Non-Linear Dirichlet Boundary Value Problems of Ordinary Differential Equations: The Shooting Method

Author

Listed:
  • Benard Audi Odongo

    (Department of Industrial and Engineering Mathematics, Technical University of Kenya, Kenya)

  • Richard Otieno Opiyo

    (Department of Pure and Applied Mathematics, Maseno University, Kenya)

  • Dancun Okeso Owego

    (Department of Pure and Applied Mathematics, Technical University of Kenya, Kenya)

  • Thomas Mboya Onyango

    (Department of Industrial and Engineering Mathematics, Technical University of Kenya, Kenya)

Abstract

In this article, a numerical technique called shooting which entails the solution of initial value problems with the single-step fourth-order RungeKutta method together with the iterative root finding secant method is formulated for use on both linear and non-linear boundary value problems of ordinary differential equations with Dirichlet boundary conditions. Two examples are illustrated. One, the solution of the linear case with its analytic counterpart is compared, and two, the non-linear case. Graphical outputs of the solutions from two MATHEMATICA codes are presented.

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Handle: RePEc:epw:ejmath:v:5:y:2024:i:5:id:14096
DOI: 10.24018/ejmath.2024.5.5.96
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