Solving high-order nonlinear Volterra-Fredholm integro-differential equations by differential transform method
نویسندگان
چکیده
In this paper, we apply the differential transformation method to high-order nonlinear VolterraFredholm integro-differential equations with separable kernels. Some different examples are considered the results of these examples indicated that the procedure of the differential transformation method is simple and effective, and could provide an accurate approximate solution or exact solution.
منابع مشابه
The 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 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 کاملSolving the fractional integro-differential equations using fractional order Jacobi polynomials
In this paper, we are intend to present a numerical algorithm for computing approximate solution of linear and nonlinear Fredholm, Volterra and Fredholm-Volterra integro-differential equations. The approximated solution is written in terms of fractional Jacobi polynomials. In this way, firstly we define Riemann-Liouville fractional operational matrix of fractional order Jacobi polynomials, the...
متن کاملAn Approximate Method for System of Nonlinear Volterra Integro-Differential Equations with Variable Coefficients
In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...
متن کاملNumerical solution of nonlinear fractional Volterra-Fredholm integro-differential equations with mixed boundary conditions
The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions. The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation. Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method. Numerical tests for demo...
متن کامل