【摘要】 针对n阶线性积分-微分方程,提出了Chebyshev小波数值法.该方法选取[0,1]上的Chebyshev小波为小波基应用Galerkin法和积分法化n阶线性积分-微分方程为代数方程求解,从而极大地简化了问题.数值解的逼近效果取决于小波基和小波系数的选取,对于小波数值解进行对比,得出了连续小波具有良好的逼近性,小波的逼近效果随着系数M的增大而越好.实例说明该方法的可行性和有效性.更多还原

【Abstract】 To the n th order linear integral-differential equation,the wavelets mothed was proposed. The continues Chebyshev wavelets constructed on[0,1] are utilized as a basis in Galerkin method and integral method to reduce the solution of the n th order linear integral-differential equation to a system of algebraic equation,thus greatly simplifing the problem. The effeciency of numerical solution is determined by the selection of the wavelets base and coefficients. The numerical solution of wavelets was compared and the continuous wavelets have a good result,higher accuracy can be achieved by increasing value of M. Illustrative example are included to demonstrate the validity and applicability of the technique.更多还原