APPLICABILITY OF SPLINE COLLOCATION TO CORDIAL VOLTERRA EQUATIONS
نویسندگان
چکیده
منابع مشابه
SPLINE COLLOCATION FOR FREDHOLM AND VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
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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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...
متن کاملSpline Collocation for Fredholm and Volterra Integro - Differential Equations
A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra integro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solution is 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 t...
متن کاملSpline Collocation for system of Fredholm and Volterra integro-differential equations
The spline collocation method is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)times(nN+3n)$ of integro-differential equations. This approximation reduces th...
متن کاملSPLINE 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...
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ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2013
ISSN: 1392-6292,1648-3510
DOI: 10.3846/13926292.2013.756072