[PDF] Top 20 Application of Triangular Functions to Numerical Solution of Stochastic Volterra Integral Equations

... [6], integral equations [3,5], integro- differential equations [4], Nonlinear Constrained Opti- mal Control Problems [9], and Volterra-Fredholm integral equations ... See full document

... oscillation equations by Saeed ...a numerical solution based on Haar wavelet method for Fredholm integral equations and the system of Volterra integral ... See full document

... TOCHASTIC Volterra integral equations (SVIEs) is a fast developing field, with applications in economics, sociology, biology, medical models and ...[1-9]. Stochastic Volterra ... See full document

... the numerical solution of integral ...to numerical solution of Fredholm integral equations of the second kind by using ...differential equations through the data ... See full document

... solving integral equations. Both scaling functions and wavelet functions are the key elements of wavelet ...solve Volterra in- tegral equations of the first kind, and ... See full document

... Block-Pulse Functions method for solving systems of linear Volterra integral equations of the second ...Block-Pulse Functions, reduces these types of equations to a linear lower ... 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

... the application of the VIM linear and nonlinear problems has been devoted by scientists and engineers, for example, non- linear systems of ordinary differential equations [11], boundary value problems [22], ... See full document

... new numerical method based on triangular functions for solving nonlinear stochastic differential equations is ...the stochastic operational matrix of triangular ... See full document

... integrate functions in ...gral equations) is that the method is reasonable in cost and also very stable against rounding er- rors as we see in the next ... See full document

... most stochastic differential and integral equation cannot be solved analytically and therefore numerical solution becomes a practical way to face this ...in numerical solutions of ... See full document

... many application in number theory and classical analysis and there are a vast literature about their applications [5, 6, ...symmetric functions of a countable set of numbers, generalising the classical ... See full document

... Thus, for determining the coefficients    i , , ( = 0,1,2,..., ) i i i k we get a homogeneous system of linear-algebraic equation in which the amount of unknowns equals 3 3 k  , the amount of equation p  1 . It is ... See full document

... ordinary differential equation, we employ the in- tegration method. This method is simple and effective, and can provide an accurate approxi- mate solution to the stochastic integral ... See full document

... In contrast to the above papers [1, 3, 7–9], the differences of this paper are as follows. Firstly, we construct a preparation theorem to deal with the nonlinear analytic functions. Secondly, the error analysis is ... See full document

... fuzzy functions by fuzzy bicubic splines interpo- lation and present a new approach based on the two-dimensional fuzzy splines interpolation and iterative method to approximate the solution of ... See full document

... piecewise functions are very es- sential tools in approximation ...and application of B-Splines is acceptable (of course for getting convenient answer we must had ... See full document

... linear Volterra integral ...of triangular functions and their operational matrix of ...the integral equation reduces to solve a recurrence ...approximate solution of ... See full document

... a numerical method for solv- ing the stochastic nonlinear volterra-fredholm integral equation (SNVFIE) driven by a standard Brownian motion ...a stochastic operational matrix (SOM) ... See full document

... The stochastic differential equations arise in many problems in mechanics, finance, biology, medical, social sciences and etc ...These equations are often dependent on a noise source, on a Gaussian ... See full document