Continuous collocation approximations to solutions of first kind Volterra equations
نویسندگان
چکیده
In this paper we give necessary and sufficient conditions for convergence of continuous collocation approximations of solutions of first kind Volterra integral equations. The results close some longstanding gaps in the theory of polynomial spline collocation methods for such equations. The convergence analysis is based on a Runge-Kutta or ODE approach.
منابع مشابه
Convergence of Numerical Method For the Solution of Nonlinear Delay Volterra Integral Equations
In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...
متن کاملA wavelet method for stochastic Volterra integral equations and its application to general stock model
In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...
متن کاملMultilevel correction for collocation solutions of Volterra integral equations with proportional delays
In this paper we propose a convergence acceleration method for collocation solutions of the linear second-kind Volterra integral equations with proportional delay qt (0 < q < 1). This convergence acceleration method called multilevel correction method is based on a kind of hybrid mesh, which can be viewed as a combination between the geometric meshes and the uniform meshes. It will be shown tha...
متن کاملDiscretization of Volterra Integral Equations
We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregul...
متن کاملIntegral Collocation Approximation Methods for the Numerical Solution of High-Orders Linear Fredholm-Volterra Integro-Differential Equations
In this paper, we employed the use of Standard Integral Collocation Approximation Method to obtain numerical solutions of special higher orders linear Fredholm-Volterra Integro-Differential Equations. Power Series, Chebyshev and Legendre's Polynomials forms of approximations are used as basis functions. From the computational view points, the method is efficient, convenient, reliable and superi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Math. Comput.
دوره 66 شماره
صفحات -
تاریخ انتشار 1997