论文标题
伯诺利正态分线多项式的应用用于某些Volterra积分方程的近似解决方案
Application of orthonormal Bernoulli polynomials for approximate solution of some Volterra integral equations
论文作者
论文摘要
在这项工作中，已经开发了一种新的方法来通过获得对溶液的渐近近似来获得线性伏尔泰型积分方程的数值解。使用经典的Bernoulli多项式，已经得出了一组正统的多项式，并且这些正顺式多项式已被用于形成一个积分的操作矩阵，该矩阵已被实现，以找到非单向Volterra积分方程的数值或精确溶液。已经解决了两个线性伏尔特拉积分和两个卷积的积分方程，以证明当前方法的有效性。已将获得的近似溶液与数值的精确解相提并论。数值解决方案的高度准确性已经确定了本方法的可信度。
In this work, a new approach has been developed to obtain numerical solution of linear Volterra type integral equations by obtaining asymptotic approximation to solutions. Using the classical Bernoulli polynomials, a set of orthonormal polynomials have been derived, and these orthonormal polynomials have been used to form an operational matrix of integration which is has been implemented to find numerical or exact solution of non-singular Volterra integral equations. Two linear Volterra integral and two convolution integral equations of second kind have been solved to demonstrate the effectiveness of present method. Obtained approximate solutions have been compared with the exact solutions for numerical values. High degree of accuracy of numerical solutions has established the credibility of the present method.
