Stability of the Spline Collocation Method for Volterra Integral Equations
نویسندگان
چکیده
منابع مشابه
SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS
The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...
متن کاملCOLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS
In this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytical solutions of a particular class of Fredholm-Volterra integral equations (FVIEs) are smooth.
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A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...
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A collocation method based on optimal nodal splines is presented for the numerical solution of linear Volterra integral equations of the second kind with weakly singular kernel. Since the considered spline operator is a bounded projector we can prove that, for sequences of locally uniform meshes, the approximate solution error converges to zero at exactly the same optimal rate as the spline app...
متن کاملcollocation method for fredholm-volterra integral equations with weakly kernels
in this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytical solutions of a particular class of fredholm-volterra integral equations (fvies) are smooth.
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ژورنال
عنوان ژورنال: Journal of Integral Equations and Applications
سال: 2001
ISSN: 0897-3962
DOI: 10.1216/jiea/996986963