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

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.


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


gfun; Maple