A homotopy perturbation method for solving a neutron transport equation

The purpose of this paper consists in the finding of the solution for a stationary transport equation using the techniques of homotopy perturbation method (HPM). The results of a numerical example illustrate the accuracy and computational efficiency of the new proposed method.     

A new method for solving nonlinear differential-difference equation

A new approach is presented which enables one to construct the exact solutions of nonlinear differential difference equations. As its application, the soliton solutions and periodic solutions of Hybrid lattice, discretized mKdV lattice and modified Volterra lattice are conveniently obtained by computing the solutions for a lattice equation introduced by Wadati.     

A regularization method for the cauchy problem of the modified Helmholtz equation

In the present paper, an iteration regularization method for solving the Cauchy problem of the modified Helmholtz equation is proposed. The a priori and a posteriori rule for choosing regularization parameters with corresponding error estimates between the exact solution and its approximation are also given. The numerical example shows the effectiveness of this method. Copyright © 2014 John Wiley & Sons, Ltd.     

A noncharacteristic cauchy problem for the heat equation

The noncharacteristic Cauchy problem for the heat equation:% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadwhadaWgaaWcbaGaamiEaiaadIhaaeqaaOGaaiikaiaadIha% caGGSaGaamiDaiaacMcacqGH9aqpcaWG1bWaaSbaaSqaaiaadshaae% qaaOGaaiikaiaadIhacaGGSaGaamiDaiaacMcacaGGSaqefeKCPfgB% aGqbbiaa-bcacaaIWaWefv3ySLgznfgDOjdaryqr1ngBPrginfgDOb% cv39gaiyqacqGFKjcHcaWG4bGae4hzIqOae4ha3hJaaeymaiaabYca% caqGTaGaeuOhIuQaeuipaWJaaeiDaiabfYda8iabf6HiLkaacYcaca% WG1bGaaiikaiaaicdacaGGSaGaamiDaiaacMcacqGH9aqpcqqHvpGA% caGGOaGaamiDaiaacMcacaGGSaGaamyDamaaBaaaleaacaWG4baabe% aakiaacIcacaaIWaGaaiilaiaadshacaGGPaGaeyypa0JaaGiYdiaa% cIcacaWG0bGaaiykaiaacYcacaWFGaGaeuOhIuQaeuipaWJaamiDai% abfYda8iabf6HiLcaa!82F8!\[u_{xx} (x,t) = u_t (x,t), 0 \le x \le {\rm{1, - }}\infty < {\rm{t}} < \infty ,u(0,t) = \varphi (t),u_x (0,t) = \psi (t), \infty < t < \infty \]is considered. This problem is well-known to be ill-posed. The well-posedness class of the problem is described and some approximation schemes are proposed. For the case of inexactly given data, a mollification method is suggested.     

A numerical method for solving the hyperbolic telegraph equation

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this article, we propose a numerical scheme to solve the one‐dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function. The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

A second-order accurate method for solving the eikonal equation

We present a numerical method for computing the signed distance to a piecewise-smooth surface defined as the zero set of a function. It is based on a marching method by Kim and a hybrid discretization of first- and second-order discretizations of the eikonal equation. If the solution is smooth at a point and at all of the points in the domain of dependence of that point, the solution is second-order accurate; otherwise, the method is first-order accurate, and computes the computes the correct entropy solution in the presence of kinks in the initial surface. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on an integrated cauchy functional equation

In characterizing the semistable law, [Shimizu reduced the problem to solving the equation ,x0 where andv are given positive measures on [0, ). In this note, we obtain a simple proof and show that some of his conditions can be weakened.     

A high order direct method for solving Poisson's equation in a disc

Summary. A direct method is developed for solving Poisson's equation on an annulus region with Hermite bicubic collocation approximation. In terms of FFT, the operation count is on an mesh. Received May 11, 1990 / Revised version received August 19, 1994     

On some method for solving a nonlinear heat equation

Some exact solutions to a nonlinear heat equation are constructed. An initial-boundary value problem is examined for a nonlinear heat equation. To construct solutions, the problem for a partial differential equation of the second order is reduced to a similar problem for a first order partial differential equation.     

A fractional Tikhonov method for solving a Cauchy problem of Helmholtz equation

In this paper, we study a fractional Tikhonov regularization method (FTRM) for solving a Cauchy problem of Helmholtz equation in the frequency domain. On the one hand, the FTRM retains the advantage of classical Tikhonov method. On the other hand, our method can prevent the effect of oversmoothing of classical Tikhonov method and conveniently control the amount of damping. The convergence error estimates between the exact solution and its regularization approximation are constructed. Several interesting numerical examples are provided, which validate the effectiveness of the proposed method.     

Implicit multiblock method for solving a kinetic equation on unstructured meshes

A parallel multiblock implementation of a second-order accurate implicit numerical method based on solving a model kinetic equation is proposed for analyzing three-dimensional rarefied gas flows. The performance of the method is illustrated by computing test examples of gas flows in a circular pipe in a wide range of Knudsen numbers. The convergence rate and scalability of the method are analyzed depending on the number of blocks in the spatial grid.     

A structure theorem for abelian quasi-ordered groups

We introduce a notion of compatible quasi-ordered groups which unifies valued and ordered abelian groups. It was proved by S.M. Fakhruddin that a compatible quasi-order on a field is always either an order or a valuation. We show here that the group case is more complicated than the field case and describe the general structure of a compatible quasi-ordered abelian group. We then define a notion of Hahn product of compatible quasi-ordered groups and generalize Hahn's embedding theorem to quasi-ordered groups. We also develop a notion of quasi-order-minimality and establish a connection with C-minimality, thus answering a question of F. Delon. Finally, we use compatible quasi-ordered groups to give an example of a C-minimal group which is neither an ordered nor a valued group.