具有奇异核的第二类混合积分方程的计算技术

A. Mahdy, M. A. Abdou, D. S. Mohamed
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引用次数: 1

摘要

本文在Banach空间L2[−1,1]×C[0,T],T<1中建立了(1+1)维混合Volterra-Fredholm积分方程(MV-FIE)的数值解。Fredholm积分项在空间L2[−1,1]中被考虑,并且它在位置上具有不连续的核。当Volterra积分项被考虑在时间C[0],T]的类中时,T<1,并且在时间上具有连续核。建立了空间L2[−1,1]×C[0],T],T<1中存在单一解的必要条件。利用变量分离技术,将MV-FIE转化为具有时间变量系数的第二类Fredholm积分方程。变量分离技术有助于作者选择合适的时间函数,以建立求解问题并获得其解的收敛条件。然后,使用Boubaker多项式方法,我们得到了一个简化的线性代数系统(LAS)。提出了Banach不动点(BFP)假设来确定LAS解的存在性和唯一性。讨论了解的收敛性和误差的稳定性。Maple 18软件用于在考虑了一些数值实验后进行一些数值计算。
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A computational technique for computing second-type mixed integral equations with singular kernels
In the present article, we establish the numerical solution for the mixed Volterra-Fredholm integral equation (MV-FIE) in (1+1) dimensional in the Banach space L 2 [− 1,1 ] × C [ 0, T ] , T < 1. The Fredholm integral term is considered in the space L 2 [− 1,1 ] and it has a discontinuous kernel in position. While the Volterra integral term is considered in the class of time C [ 0, T ] , T < 1, and has a continuous kernel in time. The necessary conditions have been established to ensure that there is a single solution in the space L 2 [− 1,1 ] × C [ 0, T ] , T < 1. By utilizing the separation of variables technique, MV-FIE is transformed to Fredholm integral equation (FIE) of the second kind with variables coefficients in time. The separation technique of variables helps the authors choose the appropriate time function to establish the conditions of convergence in solving the problem and obtaining its solution. Then, using the Boubaker polynomials method, we end up with a linear algebraic system (LAS) abbreviated. The Banach fixed point (BFP) hypothesis has been presented to determine the existence and uniqueness of the solution of the LAS. The convergence of the solution and the stability of the error are discussed. The Maple 18 software is used to perform some numerical calculations once some numerical experiments have been taken into consideration.
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CiteScore
3.10
自引率
4.00%
发文量
77
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