Barycentric Rational Interpolation Collocation Method For Volterra Type Integro-Differential Equations With Special Kernel

Volterra type integro-differential equations with special kernels are widely used in many fields of science and engineering,such as fluid mechanics,solid mechanics,heat conduction,elastic theory and heat flow.Most of these problems can be derived into initial value problems of Volterra type integro-differential equations.In recent decades,many scholars have studied the analytical solutions of this kind of equations,but most of the problems are difficult to be described by analytical solutions,which makes the innovation of numerical solutions,the improvement of numerical solutions and the application of numerical methods become the research hot topic.This article studies this kind of equation based on barycentric rational interpolation collocation method.The structure of this article is as follows:The first chapter introduces the research status of Volterra type integro-differential equations with special kernels and barycentric rational interpolation collocation method.The second chapter introduces the basic knowledge needed for the main research content of this paper.In third chapter,for the numerical solution of Volterra type integro-differential equations with convolution kernel,the discrete numerical scheme of Volterra type integro-differential equations with convolution kernel is constructed by using barycentric rational interpolation collocation method,and the global convergence theorem is obtained.Finally,selecting equidistant nodes and corresponding configuration parameters,the effectiveness of the method is verified by numerical examples.In fourth chapter,for the numerical solution of Volterra type integro-differential equation with weak singular kernel,the weak singular Volterra type integro-differential equation is transformed by variable transformation,so that the exact solution of the changed equation does not contain any singular point in any order derivative.On this basis,the discrete numerical scheme of weakly singular integro-differential equations is constructed by using barycentric rational interpolation collocation method with equal moment nodes,and the global convergence theorem is obtained.Finally,the effectiveness of the method is verified by numerical examples.The fifth chapter summarizes the work of this paper and puts forward the prospect of further research.