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1 results

  • A Spectral Method for Neutral Volterra Integro-Differential Equation with Weakly Singular Kernel

  • Yunxia Wei, Yanping Chen
  • Journal:
    Numerical Mathematics: Theory, Methods and Applications / Volume 6 / Issue 2 / May 2013
    Published online by Cambridge University Press:
    28 May 2015, pp. 424-446
    Print publication:
    May 2013

  • This paper is concerned with obtaining an approximate solution and an approximate derivative of the solution for neutral Volterra integro-differential equation with a weakly singular kernel. The solution of this equation, even for analytic data, is not smooth on the entire interval of integration. The Jacobi collocation discretization is proposed for the given equation. A rigorous analysis of error bound is also provided which theoretically justifies that both the error of approximate solution and the error of approximate derivative of the solution decay exponentially in L∞ norm and weighted L2 norm. Numerical results are presented to demonstrate the effectiveness of the spectral method.