Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

Advances in Difference Equations

article

Moosavi Noori, Seyyedeh Roodabeh¹  Taghizadeh, Nasir¹ 

[1] Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan

关键词: Modified differential transform method;    Laplace transform;    Padé approximation;    Pantograph equation;    Exact solutions;   

DOI  :  10.1186/s13662-020-03107-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

【 授权许可】

CC BY