A Sumudu based algorithm for solving differential equations. (English) Zbl 1187.34015

Zhang, Jun

Comput. Sci. J. Mold. 15, No. 3(45), 303-313 (2007).

Summary: An algorithm based on Sumudu transform is developed. The algorithm can be implemented in computer algebra systems like {tt Maple}. It can be used to solve differential equations of the following form automatically without human interaction
\[ \sum^m_{i=0} p_i(x)y^{(i)}(x)=\sum^k_{j=0} q_j(x)h_j(x), \] where \(p_i(x)\) \((i = 0,1,\dots,m)\) and \(q_j(x)\) \((j = 0,1,\dots k)\) are polynomials. \(h_j(x)\) are non-rational functions, but their Sumudu transforms are rational. \(m\), \(k\) are nonnegative integers.

MSC:

34A45	Theoretical approximation of solutions to ordinary differential equations
34A30	Linear ordinary differential equations and systems
34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34-04	Software, source code, etc. for problems pertaining to ordinary differential equations
68W30	Symbolic computation and algebraic computation

Software:

gfun; Maple