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Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

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  • S. N. Jator
  • F. F. Ngwane
  • N. O. Kirby

Abstract

We present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second-order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method’s relative accuracy and efficiency.

Suggested Citation

  • S. N. Jator & F. F. Ngwane & N. O. Kirby, 2019. "Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-14, February.
    • Handle: RePEc:hin:jnlmpe:1535430
    DOI: 10.1155/2019/1535430
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