[PDF] Top 20 Spectral Methods for Volterra Integral Equations

... Abstract- The purpose of this paper is to introduce a novel numerical method called a legedre-collocation method to solve the Volterra integral equations of second kind. We also provide error ... See full document

... spectral methods and the corresponding error analysis have been provided recently [13, 14]; see also [15, 16] for spectral methods to pantograph-type delay differential ...collocation ... See full document

... nonlinear Volterra-Hammerstein integral ...nonlinear Volterra-Hammerstein integral ...Hammerstein integral equations and the solution can be obtained for any length of ... See full document

... integro-differential equations has been studied by Maleknejad and Mahmoudi ...traditional methods for solving nonlinear integral ...powerful methods has been presented, such as the Homotopy ... See full document

... functional equations, such an ordinary or partial differential equations, integral and integro-differential equations and stochastic ...integro-differential equations, these ... See full document

... singular integral equations ...Fredholm integral equation in ...singular Volterra-Hammerstein integral ...collocation methods based on the radial basis functions has been used ... See full document

... and Volterra integral equations using Fibonacci polynomials with hat basis functions, in order to obtain a variational problem and reduce this one to a linear system, where its solution is to find ... See full document

... Vito Volterra had to solve integro-differential equations with variable ...1930s, Volterra showed that mathematical models for some seasonal diseases, ...as integral and differential ... See full document

... In this work, Picard iteration methods with numerical integration are devised for the second kind nonlinear Vol- terra integral equations. The Picard iteration method solves the considered nonlinear ... See full document

... collocation methods (PPCM) are easily programmable and they have rapid convergent order for many equations including integral or differential ... See full document

... Changqing Yang He was born in Shanxi, China, in 1973. He received the bachelor and master degrees in mathematics from Chengdu University of Technology in 1997 and 2004, respectively. His main research interests are in ... See full document

... numerical methods for the solution of Volterra integral equations using various ...of Volterra integral equations of the second ...nonlinear Volterra ... See full document

... by Volterra integral equa- tions, for example, in fluid mechanics, bio-mechanics [16, 24, ...many methods both numerical and analytical approaches to solve nonlinear equations like as finite ... See full document

... We will refer to a θ that satisfies (D1) as a vanishing delay function (or, in short, a vanishing delay ). The linear case, θ(t) = qt = t − (1 − q)t =: t − τ (t) (0 < q < 1) (proportional delay) is also known as ... See full document

... of integral equations. These equations also occur as reformulations of other mathematical problems such as partial differential equations and ordinary differential ...of integral ... See full document

... solving Volterra integral equations of the first kind in some spaces, for example, in the triple (C,V,C) is, to a certain extent, ...stable methods. Among such methods are the ... See full document

... scaling and wavelet functions make wavelet method more efficiently than other methods such as spline ap- proximations in solving an equation. A lot of computa- tional time and storage capacity can be saved since ... See full document

... Using product integration techniques, the midpoint, Euler and trapezoidal methods for Volterra integral equation s o f the first kind with continuous kernels and the schemes developed in[r] ... See full document

... numerical methods agrees with the scheme of finding its ...multistep methods and also Obreshkov k -step methods are constructed by the same ... See full document

... kind Volterra random integral equations using two approximate methods, namely the collocation method and the method of approximating the integral ...of integral equations ... See full document