differential equation systems solver matrix

Differential equation systems solver matrix series#

Numerical examples are solved to show the applicability and the effectiveness of the method. An error estimation method is also presented by using the residual function and the exponential solutions are improved by the estimated error function. The solutions of this system give the coefficients of the desired exponential solution. Later, the main problem is reduced to a system of linear algebraic equations by aid of the collocation points, the matrix operations, and the matrix forms of the conditions. Second, the differential and integral parts of the problem are converted into matrix forms based on exponential polynomials. First, by constructing the matrix forms of the exponential polynomials and their derivatives, the desired exponential solution and its derivatives are written in matrix forms. In this paper, a collocation approach based on exponential polynomials is introduced to solve linear Fredholm- Volterra integro-differential equations under the initial boundary conditions. Yübaşı and Sezer gave a matrix method based on exponential polynomials for solutions of systems of differential equations.

Differential equation systems solver matrix series#

In recent years, integro-differential equations have solved semianalytical methods such as the homotopy perturbation method, the Taylor collocation method, the Haar functions method,, He's variational iteration technique, the power series method, the Chebyshev technique, the Legendre-spectral method, the Tau method, the Legendre multiwavelets method, the finite-difference scheme, the variational iteration method, the CAS wavelet operational matrix method, the trigonometric wavelets method, the Legendre matrix method, the Taylor polynomial approach, the Adomian method, the differential transformation method, the Galerkin method, the Bessel matrix method, the Legendre collocation method, the improved homotopy perturbation method, the modified homotopy perturbation method, and the moving least square method.