An efficient hybrid method for solving fredholm integral equations using triangular functions

Abstract

Abstract:In this paper the orthogonal triangular function (TF) based method is first applied to transform the Fredholm integral equations and Fredholm system of integral equations to a coupled system of matrix algebraic equations. The obtained system is a variant of coupled Sylvester matrix equations. A finite iterative algorithm is then applied to solve this system to obtain the coefficients used to get the form of approximate solution of the unknown functions of the integral problems. Some numerical examples are solved to illustrate the accuracy and the efficiency of the proposed hybrid method. The obtained numerical results are compared with other numerical methods and the exact solutions.

A new algorithm for solving the nonlinear Lane–Emden equations arising in astrophysics

“…A general study has been given in [10] to construct both correct and series solutions to Lane-Emden equations through ADM. In [11][12][13][14][15][16][17][18] introduced Bernstein, several methods for numerical solutions of VIDE form the unique Emden-Fowler initial value problems. In [19] approach developed to obtain analytical-numerical solutions to two separate Lane-Emden problems.…”

“…First, we set to modify (18) to an integral form then differentiating Eq. (19) twice and using the Leibniz rule, we have…”

“…If we multiply y ′ (x) in (20) by k x and add to y ″ (x) in (21) we get Eq. (18). That is the VIDE is the LEE (18) that given by:…”

“…Application of HOBW method for Lane-Emden in its integrodifferential formConsider Eq. (22) acquired from Eq (18)…”

Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

“…Numerical strategies for the SNVIE are spline collocation methods [3], Newton-Cotes methods [4], extrapolation algorithm [5], and Hermite-collocation method [6]. The most popular methods for talking about the such equations are introduced, such as homotopy asymptotic method [7], Nyström interpolant method [8], Mesh method [9], Tau method [10], Laplace transform [11], orthonormal Bernstein, and block-pulse functions [12][13][14][15][16][17].…”