Application of Rational Second Kind Chebyshev Functions for System of Integrodifferential Equations on Semi-Infinite Intervals

Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method

Application of Homotopy Analysis Method to SIR Epidemic Model

Abstract In this article, the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered. Mathematical modeling of the problem leads to a system of nonlinear ordinary differential equations. Homotopy analysis method is employed to solve this system of nonlinear ordinary differential equations

A legendre wavelet spectral collocation method for solving oscillatory initial value problems.

In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate

New construction of wavelets base on floor function.

In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a,b)[a,b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine–Cosine wavelet, Block-Pulse functions and Hybrid Fourier Block-Pulse functions to get the new representations of these functions

Nonlinear Integro-Differential Equations

. In this paper,the continuse Legendre wavelets constructed on the interval [0, 1] are used to solve the nonlinear Fredholm integrodifferential equation. The nonlinear part of integro-differential is approximated by Legendre wavelets, and the nonlinear integro-differential is reduced to a system of nonlinear equations. We give some numerical examples to show applicability of the proposed metho

Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions

Abstract In this paper, we use a combination of Legendre and Block-Pulse functions on the interval [0, 1] to solve the nonlinear integral equation of the second kind. The nonlinear part of the integral equation is approximated by Hybrid Legendre Block-Pulse functions, and the nonlinear integral equation is reduced to a system of nonlinear equations. We give some numerical examples. To show applicability of the proposed method

Nonlinear Fredholm Integral Equation of the Second Kind with Quadrature Methods

In this paper, a numerical method for solving the nonlinear Fredholm integral equation is presented. We intend to approximate the solution of this equation by quadrature methods and by doing so, we solve the nonlinear Fredholm integral equation more accurately. Several examples are given at the end of this pape

Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions

In this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. To this end, we first construct the operator of Riemann–Liouville fractional integral corresponding to this kind of Müntz functions. Then, using the Gauss–Legendre quadrature rule and by employing the roots of Müntz functions as the collocation points, we arrive at a system of algebraic equations. By solving this system, an approximate solution for the fractional-order integro-differential equation is obtained. We also construct an upper bound for the truncation error of Müntz orthogonal functions, and we analyze the error of the proposed collocation method. Numerical examples are included to demonstrate the validity and accuracy of the method