Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
نویسندگان
چکیده
منابع مشابه
Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of second kind with a weakly singular kernel. We use some function transformation and variable transformations to change the equation into a new Volterra integral equation defined on the standard interval [−1, 1], so that the solution of the new equation possesses better regularity and the Jacobi or...
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Abstract This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel φ(t, s) = (t − s)−μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233: 938– 950], the error analysis for this approach is carried out for 0 < μ < 1/2 under the assumption that the underlying solution is smooth. It is noted that there is a ...
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A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2010
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-09-02269-8