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Power series solutions for non-linear PDE's
Proceedings of the 2003 international symposium on Symbolic and algebraic computation, 2003This paper describes an algorithmic method iterative method for searching power series solutions of a partial differential equation. Power series expansions considered have support in some convex cone of RN. We do this by introducing a N-variables analog of the Newton polygon construction, used in the case of ordinary differential equations.
F. Aroca, J. Cano, Françoise Jung
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Annual Meeting Optical Society of America, 1989
The real exponential series approach used to solve baseband nonlinear evolution equations is suitably modified to solve complex nonlinear evolution equations describing envelope propagation in a cubically nonlinear, dispersive optical fiber. The essence of the real exponential method is to build up the solution to the nonlinear (real) PDE from real ...
Fakar Daoud, Partha P. Banerjee
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The real exponential series approach used to solve baseband nonlinear evolution equations is suitably modified to solve complex nonlinear evolution equations describing envelope propagation in a cubically nonlinear, dispersive optical fiber. The essence of the real exponential method is to build up the solution to the nonlinear (real) PDE from real ...
Fakar Daoud, Partha P. Banerjee
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SSRN Electronic Journal, 2013
We provide an exact Taylor’s series expansion without the remainder. We demonstrate the extreme usefulness of this contribution by using it to obtain very simple solutions to PDEs.
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We provide an exact Taylor’s series expansion without the remainder. We demonstrate the extreme usefulness of this contribution by using it to obtain very simple solutions to PDEs.
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Communications in Nonlinear Science and Numerical Simulation, 2018
Abstract A counterexample is given to show that the product rule of the Caputo fractional derivatives does not hold except on a special point. The function-expansion method of separation variable proposed by Rui[Commun Nonlinear Sci Numer Simulat 47 (2017) 253–266] based on the product rule must be modified.
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Abstract A counterexample is given to show that the product rule of the Caputo fractional derivatives does not hold except on a special point. The function-expansion method of separation variable proposed by Rui[Commun Nonlinear Sci Numer Simulat 47 (2017) 253–266] based on the product rule must be modified.
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Fractals
This research offers a precise analytical solution for initial value problems of both linear and nonlinear fractional order partial differential equations. A new approach called the limit residual function method is developed and utilized to generate a series solution for the equations.
AHMAD EL-AJOU, ALIAA BURQAN
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This research offers a precise analytical solution for initial value problems of both linear and nonlinear fractional order partial differential equations. A new approach called the limit residual function method is developed and utilized to generate a series solution for the equations.
AHMAD EL-AJOU, ALIAA BURQAN
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Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy
Mathematics, 2021A D Polyanin +2 more
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Methods for Constructing Complex Solutions of Nonlinear PDEs Using Simpler Solutions
Mathematics, 2021Alexander V Aksenov +2 more
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A method for constructing exact solutions of nonlinear delay PDEs
Journal of Mathematical Analysis and Applications, 2021A D Polyanin, Vsevolod G Sorokin
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Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays
Mathematics, 2023A D Polyanin +2 more
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