##
**Two-dimensional differential transform for partial differential equations.**
*(English)*
Zbl 1024.65093

Summary: The differential transform is a numerical method for solving differential equations. In this paper, we present the definition and operation of the two-dimensional differential transform. A distinctive feature of the differential transform is its ability to solve linear and nonlinear differential equations. Partial differential equations of parabolic, hyperbolic, elliptic and nonlinear types can be solved by the differential transform. We demonstrate that the differential transform is a feasible tool for obtaining the analytic form solutions of linear and nonlinear partial differential equation.

### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |

35K05 | Heat equation |

35L05 | Wave equation |

35A22 | Transform methods (e.g., integral transforms) applied to PDEs |

35L60 | First-order nonlinear hyperbolic equations |

### Keywords:

Poisson equation; wave equation; heat equation; nonlinear first-order hyperbolic equation; numerical examples; initial value problem; differential transform; nonlinear partial differential equation
PDF
BibTeX
XML
Cite

\textit{M.-J. Jang} et al., Appl. Math. Comput. 121, No. 2--3, 261--270 (2001; Zbl 1024.65093)

Full Text:
DOI

### References:

[1] | Chen, C.L.; Liu, Y.C., Solution of two-boundary-value problems using the differential transformation method, Journal of optimization theory and application, 99, 23-35, (1998) · Zbl 0935.65079 |

[2] | Faires, J.D.; Burden, R.L., Numerical methods, (1993), PWS Publishing Company Boston, MA · Zbl 0864.65003 |

[3] | Greenberg, M.D., Advanced engineering mathematics, (1988), Prentice-Hall Englewood Cliffs, NJ · Zbl 0673.00004 |

[4] | Hilderbrand, B.H., Advanced calculus for application, second edition, (1976), Prentice-Hall Englewood Cliffs, NJ |

[5] | Jang, M.J.; Chen, C.L., Analysis of the response of strongly non-linear damped system using differential transformation technique, Applied mathematics and computation, 88, 137-151, (1997) · Zbl 0911.65067 |

[6] | Stanley, J.F., Partial differential equations for scientists and engineers, (1982), Wiley New York · Zbl 0587.35001 |

[7] | J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huarjung University Press, Wuuhahn, China, 1986 (in Chinese) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.