Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels
نویسندگان
چکیده
منابع مشابه
Polynomial spline collocation methods for second-order Volterra integrodifferential equations
where q : I → R, pi : I → R, and ki : D → R (i = 0,1) (with D := {(t,s) : 0 ≤ s ≤ t ≤ T}) are given functions and are assumed to be (at least) continuous in the respective domains. For more details of these equations, many other interesting methods for the approximated solution and stability procedures are available in earlier literatures [1, 3, 4, 5, 6, 7, 8, 11]. The above equation is usually...
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will be employed in the analysis of the principle properties of the collocation approximations; the extension to nonlinear equations is straightforward (cf. [1, p. 225]). High-order numerical methods for VIDEs with weakly singular kernels may be found in [1,2,6,7,8]. In this note we shall consider collocation methods for VIDE (1.1), based on Brunner's approach [1]. The following method and nota...
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The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent equations to round-off errors. The singularity preserving (nonpolynomial) collocation method is known to have only local convergence. To overcome th...
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ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 1986
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/6.2.221