正交伯努利多项式在求解Volterra积分方程近似解中的应用
Application of orthonormal Bernoulli polynomials for approximate solution of some Volterra integral equations
摘要：
本文提出了一种新的方法，通过获得解的渐近逼近来获得线性Volterra型积分方程的数值解。利用经典的伯努利多项式，导出了一组标准正交多项式，并利用这些标准正交多项式构成积分运算矩阵，利用该矩阵求出了非奇异Volterra积分方程的数值解或精确解.求解了两个线性Volterra积分和两个第二类卷积积分方程，验证了本文方法的有效性。得到的近似解与数值的精确解进行了比较。高精度的数值解建立了本方法的可靠性。
英文摘要：
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.
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