Solving linear and nonlinear initial value problems by the projected differential transform method

2010 ◽  
Vol 181 (5) ◽  
pp. 848-854 ◽  
Author(s):  
Bongsoo Jang
Keyword(s):  
Initial Value Problems ◽  
Differential Transform Method ◽  
Initial Value ◽  
Transform Method ◽  
Differential Transform ◽  
Linear And Nonlinear

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

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn 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.

New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices

2019 ◽  
Vol 14 (11) ◽  
Author(s):  
Feras Yousef ◽  
Marwan Alquran ◽  
Imad Jaradat ◽  
Shaher Momani ◽  
Dumitru Baleanu
Keyword(s):  
Analytical Study ◽  
Three Dimensional ◽  
Fractional Power ◽  
Differential Transform Method ◽  
Initial Value ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Models ◽  
Fractional Differential ◽  
Fractional Power Series

Abstract Herein, analytical solutions of three-dimensional (3D) diffusion, telegraph, and Burgers' models that are equipped with three memory indices are derived by using an innovative fractional generalization of the traditional differential transform method (DTM), namely, the threefold-fractional differential transform method (threefold-FDTM). This extends the applicability of DTM to comprise initial value problems in higher fractal spaces. The obtained solutions are expressed in the form of a γ¯-fractional power series which is a fractional adaptation of the classical Taylor series in several variables. Furthermore, the projection of these solutions into the integer space corresponds with the solutions of the classical copies for these models. The results detect that the suggested method is easy to implement, accurate, and very efficient in (non)linear fractional models. Thus, research on this trend is worth tracking.

scholarly journals Application of Differential Transform Method to Integral and Integro-Differential Equations

2019 ◽  
Vol 7 (6) ◽  
Author(s):  
Sudha George ◽  
T. R. Sivakumar
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Linear And Nonlinear

In this paper, Differential Transform Method (DTM) has been used to solve some systems of linear and nonlinear Integro-differential equations. The approximate solution in the form of a series are calculated with easily computable terms. The solution obtained using this method is compared with the solution obtained using existing methods.

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