Chebyshev Differential Matrix Method For Solving Differential-algebraic Equations

Differential Algebraic Equations(DAEs)are widely used in var-ious fields of science and engineering.Over the years,finding a reliable numerical method to solve DAEs has been the basic prob-lem in mathematics calculation.Based on the differential quadra-ture method(DQM),this thesis constructs the Chebyshev differ-ential matrix method(CDM)with Lagrange interpolation function and Chebyshev-Gauss-Lobatto points for solving linear DAEs with variable coefficient.Aiming at the numerical oscillation of Lagrange interpolation in Chebyshev differential matrix method,the original algorithm was improved by using the center of gravity rational inter-polation.And then further generalize it to solving the linear partial differential algebraic equations(PDAEs)with constant coefficient by Kronecker inner product.The basic idea is exploit the weighted lin-ear combination of function values at all grid points to approximate the derivatives of a node,thus the problem of solving DAEs or P-DAEs can be transformed into solving linear algebraic equations.By solving the linear algebraic equation,we can get all the values of the grid points,and then utilize interpolation methods to get the ap-proximate solution of the DAEs or PDAEs.This method is simple in principle and has high accuracy,less amount of calculation.The numerical experiments show the effectiveness of the method.