论文标题
一种用修改的bernoulli多项式求解线性全差异方程（IDE）的新技术
A new technique to solve linear integro-differential equations (IDEs) with modified Bernoulli polynomials
论文作者
论文摘要
在这项工作中，已经提出了一种新技术，以找到线性内形分化方程的近似解。该方法基于修改的正顺序Bernoulli多项式及其操作矩阵。该方法将给定的差异方程转换为一组具有未知系数的代数方程，该方程在方程中出现的已知函数很容易获得，修改了Bernoulli多项式和操作矩阵。以所需程度的多项式形式获得近似溶液。该方法还应用于三个众所周知的全差异方程式，以证明该方法的准确性和功效。将近似解决方案的数值结果与可用的精确解决方案进行了比较。通过数值比较观察到近似的误差很小，这进一步降低了所需的显着性水平。与许多现有方法相比，方法比较简单和短。
In this work, a new technique has been presented to find approximate solution of linear integro-differential equations. The method is based on modified orthonormal Bernoulli polynomials and an operational matrix thereof. The method converts a given integro-differential equation into a set of algebraic equations with unknown coefficients, which is easily obtained with help of the known functions appearing in the equation, modified Bernoulli polynomials and operational matrix. Approximate solution is obtained in form of a polynomial of required degree. The method is also applied to three well known integro-differential equations to demonstrated the accuracy and efficacy of the method. Numerical results of approximate solution are plotted to compared with available exact solutions. Considerably small error of approximation is observed through numerical comparison, which is further reducible to a required level of significance. Method is comparatively simpler and shorter than many existing methods.
