A ccdadi method for twodimensional linear and nonlinear. Quartic bspline collocation method for solving one. Numerical solution of second order one dimensional. The given equation is decomposed into system of equations and modified cubic bspline basis functions have been used for spatial. The methods are derived from the standard centred and rotated fivepoint finite difference discretisations. Two dimensional legendre wavelets for solving timefractional telegraph equation m.
A solution to the telegraph equation by using dgj method. Solving one dimensional hyperbolic telegraph equation using cubic bspline quasiinterpolation marzieh dosti and alireza nazemi abstractin this paper, the telegraph equation is solved numer ically by cubic bspline quasiinterpolation. A numerical study of two dimensional hyperbolic telegraph. In dehghan and shokri have solved two dimensional telegraph equation with variable coefficients. Solving 1d telegraphers equation by reduction to two. A numerical study of onedimensional hyperbolic telegraph. A fast finite difference method for twodimensional space. Heat or diffusion equation in 1d derivation of the 1d heat equation separation of variables refresher.
Onedimensional secondorder hyperbolic telegraph equation was formulated using ohms law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method rdtm. Mei chapter two one dimensional propagation since the equation. These schemes are secondorder accurate both in space and time. Pdf the telegraph equation and its solution by reduced. Accordingly, two dimensional statistical hydrodynamics is important for meteorology to model intermediatescale ows in atmosphere see figures6. An algorithm based on a new dqm with modified extended.
Download download engineering mechanics centroid solved problems pdf read online read online engineering mechanics centroid solved problems pdf centroid formula sheet pdf centroid sample problems with solution centroids and center of gravity examples centroid problems solution centroids and center of gravity sample problems centroid and center of gravity pdf centre of gravity formula pdf. It is based on collocation of modified cubic bspline basis functions over the finite elements. We solve a two dimensional telegraph equation with anisotropic parameters, which models the propagation of electromagnetic waves in the earthionosphere waveguide, in the frequency range 0. Chapter 1 derivation of telegraphers equations and. Using the operational matrices of integral and derivative, we reduce the problem to a set of linear algebraic equations. The adomian decomposition method applied to telegraph equation consider the onedimensional nonlinear telegraph equation of the form. Since various initial and boundary value problems exist in two dimensional reactiondiffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Solution of some fractional order telegraph equations. Pdf solution for the nonlinear telegraph equation with. In this article, we propose a numerical scheme to solve the onedimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate. Numerical solution of hyperbolic telegraph equation using.
Differential transformation method for solving onespace. Applying generalized two dimensional differential transform with. The fractional telegraph equation has recently been considered by many authors. Numerical solution for nonlinear telegraph equation 245 to solve equation 5 by adomian decomposition method, the solution u is represented by an infinite series given by. The telegraph equation is a very important analytical tool that gives the temporal.
Chaurasia c a isro telemetry, tracking and command network istrac, bangalore 560058, india b department of mathematics, university of petroleum and energy studies, dehradun 247008, india. The results are generalized to allow for the earths sphericity and the horizontal inhomogeneity of the waveguide. A solution to the telegraph equation by using dgj method murat sari1, abdurrahim gunay2, gurhan gurarslan2 1department of mathematics, faculty of art and science, pamukkale university, 20070 denizli, turkey. With this approach, finding the solution of twodimensional hyperbolic telegraph equation is transformed to finding the solution of two algebraic system of equations. The numerical study of a hybrid method for solving. Reduced differential transform method to solve two and. In present investigation, least square homotopy perturbation technique is employed to furnish the analytical solutions of multi dimensional linearnonlinear pdes partial differential equations. The proposed ccdadi method is secondorder accurate in time variable and sixthorder accurate in space variable. Abstract in this study, a robust hybrid method is used as an alternative method. Solution of the nonlinear telegraph equation using lattice. The equations come from oliver heaviside who developed the transmission line model in the 1880s.
Twodimensional nonlinear reaction diffusion equation with. Consider secondorder two space dimensional linear hyperbolic telegraph equation of the form corresponding author. Engineering mechanics centroid solved problems pdf telegraph. The resulting system of odes in time subsequently have been solved by ssprk43 scheme. A numerical study of one dimensional hyperbolic telegraph equation 63 was proposed in 37 to solve this equation.
For example, fucik and mawhin studied on generalized periodic solutions of one dimensional nonlinear telegraph equation of the form 1. In this paper, we mainly focus to study the cranknicolson collocation spectral method for twodimensional 2d telegraph equations. For the two dimensional hyperbolic telegraph equations, the combination of fdqpdq in space and time directions is preferable. Can i safely plug a two prong plug into an extension cord with a ground socket. In this article we propose a numerical scheme to solve the one. For this purpose, we first establish a cranknicolson collocation spectral model based on the chebyshev polynomials for the 2d telegraph equations. Abstract in this chapter, we discuss the transmission line theory and its application to the. In 9, an explicit difference scheme has been discussed for the numerical solution of the linear hyperbolic equation of the form eq. Derivation of the telegraph equation model an in nitesmal piece of telegraph wire as an electrical circuit which consists of a resistor of resistance rdx and a coil of inductance ldx. Two dimensional legendre wavelets for solving timefractional telegraph equation volume 6 issue 2 m. In addition, for two colliding nonlinear solutions they holds the superposition principle. Numerical solution of twodimensional telegraph equations. Differential quadrature method dqm is a numerical discretization technique for. The telegraphers equations or just telegraph equations are a pair of coupled, linear partial differential equations that describe the voltage and current on an electrical transmission line with distance and time.
A numerical study of two dimensional hyperbolic telegraph equation. A new solution procedure for the nonlinear telegraph equation. One dimensional secondorder hyperbolic telegraph equation was formulated using ohms law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method rdtm. A numerical method for solving the hyperbolic telegraph.
In this paper, laplace decomposition method, which is combined form of the laplace transform method and the adomian decomposition method, used to solve the two space dimensional nonlinear telegraph equation as. Numerical solution of onedimensional telegraph equation. This technique is based on the unique combination of wellestablished theories of least square approximation and homotopy perturbation approximation. It is shown that the resonance character of reflection from the ionosphere at. The telegraph equation was developed by oliver heaviside in the 1880s, which describes the distance and time on an electric transmission line with voltage and current. Explicit group iterative methods for the solution of.
The present paper uses new approach and methodology to solve second order one dimensional hyperbolic telegraph equation numerically by bspline collocation method. In this work it is shown the application of the generalized finite difference method gfdm for solving numerically the telegraph equation in two and threedimensional spaces. Numerical experiments show that the fast method has a significant reduction of cpu time, from two months and eight days as consumed by the traditional method to less than 40 minutes, with less than one tenthousandth of the memory required by the traditional method, in the context of a two dimensional spacefractional diffusion equation with. In this article, we mainly develop a reduced order extrapolating model for the solution coefficient vectors of the classical collocation spectral ccs scheme to the two dimensional 2d telegraph equation by means of a proper orthogonal decomposition pod. Jafaris method dgj, for twospace dimensional telegraph equation, dehghan, ghesmati 5 used a numerical method based on the boundary integral equation bie and an application of the dual. A numerical method based on the interpolating scaling. Heat or diffusion equation in 1d university of oxford. The advantage of the use of dqm both in space and time directions lies in the fact that the solution can be obtained at a required time level by solving one system.
Numerical solution for nonlinear telegraph equation by. Numerical solution of 2d telegraph equation with variable coefficients has been tackled by dehghan and shorki. In this paper, a combined compact finite difference method ccd together with alternating direction implicit adi scheme is developed for twodimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. Two and threedimensional telegraph equation reduced differential trans form method exact solution. Pdf twodimensional legendre wavelets for solving time. Dehghan and shokri 7 developed a numerical method to solve the one dimensional telegraph equation using thin plate splines tps radial basis function rbf. The results are generalized to allow for the earths sphericity and the. Least square homotopy solution to hyperbolic telegraph. The telegraph equation and its solution by reduced. Numerical solution of telegraph equation with variable coefficient, was. We present here, three dimensional haar wavelet based method for solving well known two dimensional telegraph equation, by approximating higher order mixed derivatives by a series of higher dimensional haar wavelet functions, which are integrated subsequently to get wavelet approximation of the solution. Differential quadrature solution of hyperbolic telegraph. In this paper, we mainly focus to study the cranknicolson collocation spectral method for two dimensional 2d telegraph equations. Mohammadi skip to main content we use cookies to distinguish you from other users and to provide you with a better experience on our websites.
Generalized telegraph equations and pseudorelativistic invariance. A reduced order extrapolating technique of solution. Derivation of spdes for correlated random walk transport. In this paper, we develop an accurate and efficient legendre wavelets method for numerical solution of the well known timefractional telegraph equation.
Lagranges operational approach for the approximate solution of two dimensional hyperbolic telegraph equation subject to dirichlet boundary. Telegraph equation, latticeboltzmann, tanh and riccati methods 1 introduction in this paper we deal with the nonlinear telegraph equation nteq. Rubinstein3 1university of bologna, bologna, italy. Then, in the following two sections, a stochastic version of the telegraph equation is derived and a stochastic version of the two dimensional linear transport equation is derived. Reduced differential transform method to solve two and three. Solving onedimensional hyperbolic telegraph equation. A cranknicolson collocation spectral method for the two. Numerical solution for fractional model of telegraph equation. Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Lagranges operational approach for the approximate solution of two. The method consists of expanding the required approximate solution as the elements of shifted chebyshev polynomials.
612 1640 256 141 1100 401 84 503 396 123 1190 860 222 90 902 684 1256 412 428 1159 701 1554 1502 1422 154 515 184 595 783 1328 423 1089 1109 550 435 10