A Sumudu based algorithm for solving differential equations.

*(English)*Zbl 1187.34015Summary: 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

$$\sum _{i=0}^{m}{p}_{i}\left(x\right){y}^{\left(i\right)}\left(x\right)=\sum _{j=0}^{k}{q}_{j}\left(x\right){h}_{j}\left(x\right),$$

where ${p}_{i}\left(x\right)$ $(i=0,1,\cdots ,m)$ and ${q}_{j}\left(x\right)$ $(j=0,1,\cdots k)$ are polynomials. ${h}_{j}\left(x\right)$ are non-rational functions, but their Sumudu transforms are rational. $m$, $k$ are nonnegative integers.

##### MSC:

34A45 | Theoretical approximation of solutions of ODE |

34A30 | Linear ODE and systems, general |

34A25 | Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.) |

34-04 | Machine computation, programs (ordinary differential equations) |

68W30 | Symbolic computation and algebraic computation |