Approximation of Systems of Volterra Integro-Differential Equations Using the New Iterative Method
نویسنده
چکیده
In this paper, the new iterative method with a reliable algorithm is applied to the systems of Volterra integro-differential equations. The method is useful for both linear and nonlinear equations. By using this method, the solutions are obtained in series form. Two linear and one nonlinear system of the equations are given to verify the reliability and efficiency of the method. Beside this, the comparison of the exact solution with the approximated solution by the method is illustrated by the graphs.
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 کاملA new reproducing kernel method for solving Volterra integro-dierential equations
This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the...
متن کاملApproximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method
This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...
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 کاملSpline Collocation for system of Fredholm and Volterra integro-differential equations
The spline collocation method is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)times(nN+3n)$ of integro-differential equations. This approximation reduces th...
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 کامل