Numerical Solution of Mixed Volterra – Fredholm Integral Equation Using the Collocation Method

Abstract

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained from the numerical experiments in order to investigate the accuracy and the efficiency of scheme.

Application of HAM for Nonlinear Integro-Differential Equations of Order Two

“…Then, this has been extended by Wazwaz [3] [4] to Volterra integral equation and to boundary value problems for higher-order integro-differential equations. There are many other methods developed by different researchers for linear and nonlinear IDEs with initial, boundary or mixed conditions, for instance homotopy analysis method (HAM) developed by Liao [5] [6] [7], modified HAM [8], q-HAM [9], new development of HAM [10], homotopy perturbation method (HPM) developed by Ji-Huan He [11] [12], HPM for nonlinear differential-difference equations [13], HPM for nth-Order Integro-Differential Equations [14], collocation method [15], new boundary element method [16], Linear Programming Method [17], Laplace Decomposition Algorithm [18], polynomial approximations [19], Wavelet Galerkin method [20], and so on.…”

Numerical Computation of Mixed Volterra–Fredholm Integro-Fractional Differential Equations by Using Newton-Cotes Methods

“…The approximate methods have gained importance to prevent this difficulty. Many methods evaluate the approximate solution of integro-fractional differential equations; see references [9][10][11][12][13][14][15][16][17][18][19]. In [11], the author utilized modified Navot-Simpson's quadrature for solving second-kind Volterra integral equations of singular type.…”