Application of the Hybrid Methods to Solving Volterra Integro-Differential Equations
نویسندگان
چکیده
Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra integro-differential equations. The way for defining the coefficients of the suggested method is also given. Keywords—Integro-differential equations, initial value problem, hybrid methods, predictor-corrector method
منابع مشابه
Application of the block backward differential formula for numerical solution of Volterra integro-differential equations
In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...
متن کاملThe combined reproducing kernel method and Taylor series for solving nonlinear Volterra-Fredholm integro-differential equations
In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...
متن کاملA new approach for solving fuzzy linear Volterra integro-differential equations
In this paper, a fuzzy numerical procedure for solving fuzzy linear Volterra integro-differential equations of the second kind under strong generalized differentiability is designed. Unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method and other numerical methods.Error ana...
متن کاملDirect method for solving nonlinear two-dimensional Volterra-Fredholm integro-differential equations by block-pulse functions
In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...
متن کاملDirect method for solving nonlinear two-dimensional Volterra-Fredholm integro-differential equations by block-pulse functions
In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...
متن کامل