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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
  • Richard Otieno Opiyo
  • Dancun Okeso Owego
  • Thomas Mboya Onyango

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.

Suggested Citation

  • Benard Audi Odongo & Richard Otieno Opiyo & Dancun Okeso Owego & Thomas Mboya Onyango, 2024. "On the Numerical Solution of Linear and Non-Linear Dirichlet Boundary Value Problems of Ordinary Differential Equations: The Shooting Method," European Journal of Mathematics and Statistics, European Open Science, vol. 5(5), pages 7-12, September.
    • Handle: RePEc:epw:ejmath:v:5:y:2024:i:5:id:14096
    DOI: 10.24018/ejmath.2024.5.5.96
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