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A Comparative Study of Variational Iteration Method and He-Laplace Method  [PDF]
Hradyesh Kumar Mishra
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.310174
Abstract: In this paper, variational iteration method and He-Laplace method are used to solve the nonlinear ordinary and partial differential equations. Laplace transformation with the homotopy perturbation method is called He-Laplace method. A comparison is made among variational iteration method and He-Laplace. It is shown that, in He-Laplace method, the nonlinear terms of differential equation can be easily handled by the use of He’s polynomials and provides better results.
He-Laplace Method for Linear and Nonlinear Partial Differential Equations
Hradyesh Kumar Mishra,Atulya K. Nagar
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/180315
Abstract: A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round-off errors.
Modified Adomain Decomposition Method for the Generalized Fifth Order KdV Equations  [PDF]
Huda O. Bakodah
American Journal of Computational Mathematics (AJCM) , 2013, DOI: 10.4236/ajcm.2013.31008
Abstract:

New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.

Classroom note: Fourier method for Laplace transform inversion  [PDF]
M. Iqbal
Advances in Decision Sciences , 2001, DOI: 10.1155/s1173912601000141
Abstract: A method is described for inverting the Laplace transform. The performance of the Fourier method is illustrated by the inversion of the test functions available in the literature. Results are shown in the tables.
Stein's method and the Laplace distribution  [PDF]
John Pike,Haining Ren
Mathematics , 2012,
Abstract: Using Stein's method techniques, we develop a framework which allows one to bound the error terms arising from approximation by the Laplace distribution and apply it to the study of random sums of mean zero random variables. As a corollary, we deduce a Berry-Esseen type theorem for the convergence of certain geometric sums. Our results make use of a second order characterizing equation and a distributional transformation which is related to zero-biasing.
Laplace transformation method for the Black-Scholes equation  [PDF]
Hyoseop Lee,Dongwoo Sheen
Mathematics , 2009,
Abstract: In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thom\'ee (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally parallelizable. It is shown that the method is very efficient for calculating various options. Existence and uniqueness properties of the Laplace transformed Black-Scholes equation are analyzed. Also a transparent boundary condition associated with the Laplace transformation method is proposed. Several numerical results for various options under various situations confirm the efficiency, convergence and parallelization property of the proposed scheme.
The DJ method for exact solutions of Laplace equation  [PDF]
M. Yaseen,M. Samraiz,S. Naheed
Physics , 2012,
Abstract: In this paper, the iterative method developed by Daftardar-Gejji and Jafari (DJ method) is employed for analytic treatment of Laplace equation with Dirichlet and Neumann boundary conditions. The method is demonstrated by several physical models of Laplace equation. The obtained results show that the present approach is highly accurate and requires reduced amount of calculations compared with the existing iterative methods.
Enclosure method for the p-Laplace equation  [PDF]
Tommi Brander,Manas Kar,Mikko Salo
Mathematics , 2014, DOI: 10.1088/0266-5611/31/4/045001
Abstract: We study the enclosure method for the p-Calder\'on problem, which is a nonlinear generalization of the inverse conductivity problem due to Calder\'on that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, where the inclusion is modelled as a jump in the conductivity. The result is based on a monotonicity inequality and the properties of the Wolff solutions.
3He NMR in porous media: Inverse Laplace transformation  [PDF]
R. R. Gazizulin,A. V. Klochkov,V. V. Kuzmin,K. R. Safiullin,M. S. Tagirov,A. N. Yudin
Physics , 2010,
Abstract: For the first time the inverse Laplace transform was applied for analysis of 3He relaxation in porous media. It was shown that inverse Laplace transform gives new information about these systems. The uniform-penalty algorithm has been performed to obtain the 3He relaxation times distribution in pores of clay sample. It is possible to obtain pores' sizes distribution by using applicable model. Keywords: inverse Laplace transform, uniform-penalty algorithm, liquid 3He, 3He, He3, He-3, helium-3, pulse nuclear magnetic resonance, clay, porous media.
Exact solutions of Laplace equation by differential transform method  [PDF]
M. Jamil Amir,M. Yaseen,Rabia Iqbal
Mathematics , 2013,
Abstract: In this paper, we solve Laplace equation analytically by using differential transform method. For this purpose, we consider four models with two Dirichlet and two Neumann boundary conditions and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.
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