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Numerical solution of eighth order boundary value problems in reproducing Kernel space

Abstract

In this paper, the approximate solutions to the eighth-order boundary-value problems are presented using the reproducing kernel space method. The procedure is applied on both linear and nonlinear problems. Searching least value (SLV) method is investigated for nonlinear boundary value problems. The argument is based on the reproducing kernel space \(W_{2}^{9}[a,b]\). The approach provides the solution in the form of a convergent series with easily computable components. Analytical results are given for several examples to illustrate the implementation and efficiency of the method. A comparison of the results obtained by the present method with results obtained by other methods reveals that the present method is more effective and convenient.

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Correspondence to Ghazala Akram.

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Akram, G., Rehman, H.U. Numerical solution of eighth order boundary value problems in reproducing Kernel space. Numer Algor 62, 527–540 (2013). https://doi.org/10.1007/s11075-012-9608-4

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  • DOI: https://doi.org/10.1007/s11075-012-9608-4

Keywords

  • Exact solution
  • Approximate solution
  • Gram–Schmidt orthogonal process
  • Reproducing Kernel
  • Searching Least Value (SLV) method