The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes
نویسندگان
چکیده
منابع مشابه
The Numerical Solution of Weakly Singular Volterra Integral Equations By Collocation on Graded Meshes
Since the solution of a second-kind Volterra integral equation with weakly singular kernel has, in general, unbounded derivatives at the left endpoint of the interval of integration, its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates. In this paper we investigate the convergence rates with respect to graded meshes, and we discuss the pr...
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In this paper, a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method. In this method, a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution. Error analysis of this method is also ...
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متن کاملCollocation Solutions of a Weakly Singular Volterra Integral Equation
p(t, s) := s tμ , (1.2) where μ > 0, K(t, s) is a smooth function and g is a given function, can arise, e.g., in heat conduction problems with mixed boundary conditions ([2], [10]). The case when K(t, s) = 1 has been considered in several papers. The following lemma summarizes the analytical results for (1.1) in the case K(t, s) = 1. Lemma 1.1. (a) [12] Let μ > 1 in (1.2). If the function g bel...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1985
ISSN: 0025-5718
DOI: 10.2307/2008134