Numerical Solution of Convection-Diffusion Integro-Differential Equations with a Weakly Singular Kernel
نویسندگان
چکیده
Many mathematical formulations of physical phenomena contain integro-differential equations. In this paper a numerical method is developed to solve the convection-diffusion integro-differential equations with a weakly singular kernel using the cubic B-spline collocation method. These equations occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors etc. The proposed method is based on collocation of cubic B-spline over finite elements, so that the continuity of the dependent variable and its first two derivatives throughout the solution range is obtained. The backward Euler scheme is used in time direction and the cubic B-spline collocation method is used for the spatial derivative. Some numerical examples are considered to illustrate the efficiency of the method developed. It has been observed that the numerical results efficiently approximate the exact solutions.
منابع مشابه
Application of Tau Approach for Solving Integro-Differential Equations with a Weakly Singular Kernel
In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....
متن کاملWavelet-based numerical method for solving fractional integro-differential equation with a weakly singular kernel
This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel. First, a collocation method based on Haar wavelets (HW), Legendre wavelet (LW), Chebyshev wavelets (CHW), second kind Chebyshev wavelets (SKCHW), Cos and Sin wavelets (CASW) and BPFs are presented f...
متن کاملA spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations
In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...
متن کاملA Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...
متن کاملNumerical solution of Convection-Diffusion equations with memory term based on sinc method
In this paper, we study the numerical solution of Convection-Diffusion equation with a memory term subject to initial boundary value conditions. Finite difference method in combination with product trapezoidal integration rule is used to discretize the equation in time and sinc collocation method is employed in space. The accuracy and error analysis of the method are discussed. Numeric...
متن کامل