论文信息 - A simple approach to the particular solution of constant coefficient ordinary differential equations

A simple approach to the particular solution of constant coefficient ordinary differential equations

An eigenfunction approach to compute the particular solution of constant coefficient ordinary differential equations is presented. It is shown that the exponentials are the eigenfunctions of such equations. Solutions corresponding to products of powers and exponentials are obtained. The singular case is studied and a fast algorithm for its implementation is presented.

Manuel Duarte Ortigueira

[1] Michael J. Roberts,et al. Signals and Systems: Analysis Using Transform Methods and MATLAB , 2003 .

[2] C. A. Grimm. Particular Solutions of Linear Difference Equations with Constant Coefficients , 1963 .

[3] Ji-Teng Jia,et al. On particular solution of ordinary differential equations with constant coefficients , 2013, Appl. Math. Comput..

[4] Weiming Wang,et al. A mechanical algorithm for solving ordinary differential equation , 2006, Appl. Math. Comput..

[5] Shishen Xie,et al. An algorithm for solving a nonlinear integro-differential equation , 2000, Appl. Math. Comput..

[6] A. Zemanian,et al. Distribution theory and transform analysis , 1966 .

[7] Edward B. Saff,et al. Fundamentals of Differential Equations , 1989 .

[8] D. Westreich. Partial fraction expansion without derivative evaluation , 1991 .

[9] Manuel Duarte Ortigueira,et al. Fractional Calculus for Scientists and Engineers , 2011, Lecture Notes in Electrical Engineering.

[10] Ramesh C. Gupta. Classroom Note: On Particular Solutions of Linear Difference Equations with Constant Coefficients , 1998, SIAM Rev..