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Search Results: 1 - 10 of 14749 matches for " Nonlinear Partial Differential Equations "
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Similarity Reduction of Nonlinear Partial Differential Equations  [PDF]
Amnah S. Al-Johani
Journal of Applied Mathematics and Physics (JAMP) , 2014, DOI: 10.4236/jamp.2014.23003

In this work, the HB method is extended to search for similarity reduction of nonlinear partial differential equations. This method is generalized and will apply for a (2 + 1)-dimensional higher order Broer-Kaup System. Some new exact solutions of Broer-Kaup System are found.

The Solutions for the Eco-Epidemic Model with Homotopy Analysis Method  [PDF]
Xiurong Chen
Engineering (ENG) , 2013, DOI: 10.4236/eng.2013.510B091

In this paper, the Homotopy Analysis Method (HAM) has been used to solve an eco-epidemic model equation. The algorithm of approximate analytical solution is obtained. HAM contains the auxiliary parameterhwhich provides us with a convenient way to adjust and control convergence region and rate of solution series. The results obtained show that these algorithms are accurate and efficient for the model.

Solving p-Laplacian equations on complete manifolds
Mohammed Benalili,Youssef Maliki
Electronic Journal of Differential Equations , 2006,
Abstract: Using a reduced version of the sub and super-solutions method, we prove that the equation $Delta _{p}u+ku^{p-1}-Ku^{p^{ast }-1}=0$ has a positive solution on a complete Riemannian manifold for appropriate functions $k,K:M o mathbb{R}$.
A Note on Crank-Nicolson Scheme for Burgers’ Equation  [PDF]
Kanti Pandey, Lajja Verma
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.27118
Abstract: In this work we generate the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. Absolute error of the present method is compared to the absolute error of the two existing methods for two test problems. The method is also analyzed for a third test problem, nu-merical solutions as well as exact solutions for different values of viscosity are calculated and we find that the numerical solutions are very close to exact solution.
Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations  [PDF]
Artion Kashuri, Akli Fundo, Matilda Kreku
Advances in Pure Mathematics (APM) , 2013, DOI: 10.4236/apm.2013.33045

In this paper, we present a new method, a mixture of homotopy perturbation method and a new integral transform to solve some nonlinear partial differential equations. The proposed method introduces also He’s polynomials [1]. The analytical results of examples are calculated in terms of convergent series with easily computed components [2].

Existence the Solutions of Some Fifth-Order Kdv Equation by Laplace Decomposition Method  [PDF]
Sujit Handibag, B. D. Karande
American Journal of Computational Mathematics (AJCM) , 2013, DOI: 10.4236/ajcm.2013.31013

In this paper, we develop a method to calculate numerical and approximate solution of some fifth-order Korteweg-de Vries equations with initial condition with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to some fifth-order Kdv equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of four examples and results of the present technique have closed agreement with approximate solutions obtained with the help of (LDM).

Hamiltonian Representation of Higher Order Partial Differential Equations with Boundary Energy Flows  [PDF]
Gou Nishida
Journal of Applied Mathematics and Physics (JAMP) , 2015, DOI: 10.4236/jamp.2015.311174
Abstract: This paper presents a system representation that can be applied to the description of the interaction between systems connected through common boundaries. The systems consist of partial differential equations that are first order with respect to time, but spatially higher order. The representation is derived from the instantaneous multisymplectic Hamiltonian formalism; therefore, it possesses the physical consistency with respect to energy. In the interconnection, particular pairs of control inputs and observing outputs, called port variables, defined on the boundaries are used. The port variables are systematically introduced from the representation.
New Generalized (G'/G)-Expansion Method Applications to Coupled Konno-Oono Equation  [PDF]
Md. Nur Alam, Fethi Bin M. Belgacem
Advances in Pure Mathematics (APM) , 2016, DOI: 10.4236/apm.2016.63014
Abstract: The new generalized (G'/G)-expansion method is one of the powerful and competent methods that appear in recent time for establishing exact solutions to nonlinear evolution equations (NLEEs). We apply the new generalized (G'/G)-expansion method to solve exact solutions of the new coupled Konno-Oono equation and construct exact solutions expressed in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. The significance of obtained solutions gives credence to the explanation and understanding of related physical phenomena. As a newly developed mathematical tool, this method efficiency for finding exact solutions has been demonstrated through showing its straightforward nature and establishing its ability to handle nonlinearities prototyped by the NLEEs whether in applied mathematics, physics, or engineering contexts.
A Study of Some Nonlinear Partial Differential Equations by Using Adomian Decomposition Method and Variational Iteration Method  [PDF]
Marha M. Shehata
American Journal of Computational Mathematics (AJCM) , 2015, DOI: 10.4236/ajcm.2015.52016
Abstract: In this paper, a numerical solution of nonlinear partial differential equation, Benjamin-Bona-Mahony (BBM) and Cahn-Hilliard equation is presented by using Adomain Decomposition Method (ADM) and Variational Iteration Method (VIM). The results reveal that the two methods are very effective, simple and very close to the exact solution.
Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions  [PDF]
Nawal Abdullah Alzaid, Huda Omar Bakodah
American Journal of Computational Mathematics (AJCM) , 2018, DOI: 10.4236/ajcm.2018.82012
Abstract: In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.
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