Discrete sine gordon dynamics on networks, submitted, 2016. The name of the transient version of the sinegordon equation is a play on words on the similar form of the klein gordon equation specify a region. For more information on the numerical method and on the interpretation of these results, please, refer to our preprint. Any one has the builtin function for solving sine gordon equation or how can i find it in matlab if any.
In this paper, we develop a numerical method for the ndimensional sinegordon equation using differentiation matrices, in the theoretical frame of matrix differential equations our method avoids calculating exponential matrices, is very intuitive and easy to express, and can be implemented without toil in any number of spatial dimensions. Depending on its arguments, sin returns floatingpoint or exact symbolic results. A numerical solution for sine gordon type system slideshare. Sinegordon equation using the average vector field avf discrete. Highorder solution of onedimensional sinegordon equation using. Sine integral function for numeric and symbolic arguments. Plot symbolic expression, equation, or function matlab. Now i want to find the linear equation of a line passing through these 2 points.
In this paper, we propose a numerical scheme to solve the twodimensional dampedundamped sinegordon. Our computations were performed using matlab 7 software on a pentium iv. Based on nonlinear spectral analysis, exact nonreflecting boundary conditions are derived at two artificially introduced boundary points. Solve a coupled stationary nonlinear sinegordon equation. Inverse sine in degrees matlab asind mathworks australia. This is the range along the abscissa horizontal axis. Sine integral function matlab sinint mathworks india. Discrete gradient moving mesh solver for the 1d sinegordon equation. The main difference is that the sum of sines equation includes the phase constant, and does not include a constant intercept term.
Numerical solution to the sinegordon equation defined on. Modified cubic bspline collocation method is discussed for the numerical solution of onedimensional nonlinear sine gordon equation. Support for character vector or string inputs has been removed. To give the clear overview of this method we consider three examples of kleingordon equation and sinegordon equation. Equations 1 and 2 are actually the solutions to these pdes. The equation describes nonlinear waves in elastic media, and it also has applications in relativistic field theory drazin and. Dehghan and mirzaei used a numerical method of the boundary.
In this article, were going to explore a number of ways to calculate the sine series without actually using the sine or cosine function. The fractional sinegordon equation is considered as an interpolation between the classical sinegordon equation corresponding to. In this section, we give the basic theory of the sinegordon equation and the variety of its travelingwave solutions, as spatiotemporal models of nonlinear excitations in complex physical systems. This matlab code solves the classical nonlinear sinegordon equation on graphs. This equation is closely related to the fourier series described in fourier series. Compute the sine integral function for these numbers.
This matlab function returns the sine function of x. The sinegordon sg equation is a partial differential equation, which is defined as utt. The matlab system was used for the numerical computations. Sine of argument in degrees matlab sind mathworks italia. In this paper, we propose a numerical scheme to solve the twodimensional dampedundamped sine gordon. The method is based on collocation of modified cubic bsplines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range.
Thanks for contributing an answer to computational science stack exchange. In this paper, numerical solutions of the secondorder twodimensional sine gordon equation obtained by polynomial differential quadrature method have been discussed. The sinegordon equation has attracted wide attention over the years in the description of classical and quantum mechanical phenomena 19, and within the framework of quantumfield theory 917. If you do not specify var, the symvar function determines the variable to solve for. Several new exact travelling wave solutions with the form of jacobiamplitude function are derived for the general sinegordon equation by using some reasonable transformation. Depending on its arguments, sinint returns floatingpoint or exact symbolic results. Sep 03, 2015 newtons method for solving nonlinear systems of algebraic equations. Numerical solution to the sinegordon equation defined on the.
Furthermore, we also give a numeric solution using a splitstep algorithm, and also present two physical applications of the sinegordon equation. Im supposed to generate a 6 seconds long sine wave that has amplitude of 1. The nonlinear sine gordon equation arises in various problems in science and engineering. The given equation is decomposed into a system of equations and. Modified cubic bspline collocation method is discussed for the numerical solution of onedimensional nonlinear sinegordon equation. Of particular interest is the domain wall collision to 2d sine gordon equation which to the authors knowledge have not been presented in the literature. On multisoliton solutions of the sinegordon equation in. The representation on solutions of the sinegordon and.
Firstly, we discretize the equation by legendre spectral element in space and then discretize the time by the secondorder leapfrog method. We propose a method to deal with the general sinegordon equation. The numerical examples were calculated using a matlab program. This paper gives three new solutions to solve the 2d sinegordon equation. This code is meant as a supplement to 1, and is an implementation of a moving mesh energy preserving solver for the 1d sinegordon equation using the average vector field avf discrete gradient. Legendre spectral element method for solving sinegordon. Sine of argument in degrees matlab sind mathworks united. If f is a univariate expression or function, then min,max specifies the range for that variable. Solve algebraic equations to get either exact analytic solutions or highprecision numeric solutions. The name of the transient version of the sinegordon equation is a play on words on the similar form of the klein gordon equation. Instead, use syms to declare variables and replace inputs such as solve 2x 1,x with solve 2x 1,x. New travelling wave solutions for sinegordon equation. The matlab environment was used for the numerical computations.
Numerical solution of kleingordon and sinegordon equations. Also, if you could correct your syntax you might have better luck. Blue waters undergraduate petascale education program. In the present chapter, we consider two prototypical kleingordon models. Legendre spectral element method for solving sinegordon equation. S solve eqn,var solves the equation eqn for the variable var. In this paper, we study the legendre spectral element method for solving the sine gordon equation in one dimension.
All the results are calculated by using the symbolic calculus software matlab 20a and mathematica. Sine gordon equation using the average vector field avf discrete. Numerical simulation of twodimensional sinegordon solitons. Problem with a numerical solution of sinegordonlike. Pdf a numerical solution for sinegordon type system. In this seminar, we will introduce the sinegordon equation, and solve it.
Of particular interest is the domain wall collision to 2d sinegordon equation which to the authors knowledge have not been presented in the literature. Several new exact travelling wave solutions with the form of jacobiamplitude function are derived for the general sine gordon equation by using some reasonable transformation. The eqworld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations. We propose a method to deal with the general sine gordon equation. Sine of angle, returned as a realvalued or complexvalued scalar, vector, matrix, or nd array of the same size as x. Newtons method for solving nonlinear systems of algebraic equations. The nonlinear sinegordon equation arises in various problems in science and engineering. I am curious if your original equationfunction that you are trying to plot is yt25 sin3 t. Now im confused with the sinegordon theory which is also 2 dimensional like equation 1. These notes, prepared for the durham summer school 2002, are complementary to the monograph of e. A matlab differentiation matrix suite applied mathematics.
Numerical solution of nonlinear sinegordon equation by. Is there any function in matlab that accepts coordinates of two points an gives the related linear equation back. Finding the equation of a line passing 2 points matlab. Because these numbers are not symbolic objects, sinint returns floatingpoint results. Derivation of the explicit scheme formula for the sine gordon system. The sine function usually expressed in programming code as sinth, where th is an angle in radians is one of the basic functions in trigonometry. Discrete singular convolution method for the sinegordon. Numerical solution of kleinsinegordon equations by spectral method coupled. The opposite side is the side opposite to the angle of interest, in this case side a the hypotenuse is the side opposite the right angle, in this. You can solve algebraic equations, differential equations, and differential algebraic equations daes.
The proposed method provides a reliable technique which is computer oriented if compared with traditional techniques. Geometric numerical integration is synonymous with structurepreserving integration of ordinary differential equations. We focus, in particular, on two of their principal solutions, namely the kinklike heteroclinic connections and the timeperiodic, exponentially localized in space breather waveforms. This paper gives three new solutions to solve the 2d sine gordon equation. Convert a secondorder differential equation into a system of differential equations that can be solved using the numerical solver ode45 of matlab. Sinegordon equations, numerical simulation, matlab. If f is an equation or function of two variables, then min,max specifies the range for both variables, that is the ranges along both the abscissa and the ordinate.
Gnicodes matlab programs for geometric numerical integration. Example 1 25 we consider the nonlinear kleingordon equation with, and in the interval with the initial conditions. The sine of an acute angle is defined in the context of a right triangle. Numerical solution of kleinsinegordon equations by.
Consider the onedimensional sinegordon nonlinear hyperbolic equation 1. Numerical simulation of the solution to the sine gordon equation on the whole real axis is considered in this paper. The sine gordon equation has attracted wide attention over the years in the description of classical and quantum mechanical phenomena 19, and within the framework of quantumfield theory 917. These solver functions have the flexibility to handle complicated. The sinegordon equation firstly appeared in the study of the differential geometry of surfaces with gaussian curvature k. To give the clear overview of this method we consider three examples of klein gordon equation and sine gordon equation. The representation on solutions of the sinegordon and klein. For analytic solutions, use solve, and for numerical solutions, use vpasolve. If this is the case, then you need to change your parenthesis so that sin is a function of the independent variable x or t. Our method avoids calculating exponential matrices, is very intuitive and easy to express, and can be implemented without toil in any number of spatial dimensions. If this is the case, then you need to change your parenthesis so that sin is a function of the independent variable.
We study the stability and convergence of the method and show the convergence of our method. Collision of wave packets in the sinegordon equation universiteit. In this section, we give the basic theory of the sine gordon equation and the variety of its travelingwave solutions, as spatiotemporal models of nonlinear excitations in complex physical systems. Adaptive energy preserving methods for partial differential equations.
Oct 07, 2014 im supposed to generate a 6 seconds long sine wave that has amplitude of 1. Notes on the sine gordon equation david gablinger january 31, 2007 abstract in this seminar, we will introduce the sine gordon equation, and solve it using a baecklund transfomation. Writing a matlab program to solve the advection equation. Contribute to saulwiggincomputational engineeringwithmatlab development by creating an account on github. But avoid asking for help, clarification, or responding to other answers. Y asindx returns the inverse sine sin1 of the elements of x in degrees. Numerical solution of kleinsinegordon equations by spectral. Solving an equation containing sine and cosine matlab. In section 5 we also explore the relationship between the lyapunov equations and the sylvester equation and show how their solutions are related to each other in a simple but interesting way.
Problem with a numerical solution of sinegordon like coupled equations in matlab. Computationalengineeringwithmatlabsinegordonsoliton. This matlab code solves the classical nonlinear sine gordon equation on graphs. Numerical simulation of the solution to the sinegordon equation on the whole real axis is considered in this paper. Compared with previous solutions, our solutions are more general than some of the previous. For real values of x in the interval 1, 1, asindx returns values in the interval 90, 90. Numerical simulation of the ndimensional sinegordon. Furthermore, we also give a numeric solution using a splitstep algorithm, and also present two physical applications of the sine gordon equation. Any one has the builtin function for solving sinegordon equation or how can i find it in matlab if any. The sinegordon equation is a nonlinear partial differential equation. Dehghan and shokri solved a onedimensional sinegordon equation using collocation points and approximating the solution using thin plate splines radial basis function. Kaya 7 has implemented the decomposition method for solving the sinegordon equation by using a number of initial values in the form of. Were going to play with the concepts of sine series, iterations, vectorizing programs.
In mathematics, the sine is a trigonometric function of an angle. I am curious if your original equation function that you are trying to plot is yt25 sin3 t. Extended capabilities tall arrays calculate with arrays that have more rows than fit in memory. The three sides of the triangle are named as follows. Open live script gausslaguerre quadrature evaluation points and weights. In this paper, we develop a numerical method for the ndimensional sine gordon equation using differentiation matrices, in the theoretical frame of matrix differential equations. In this paper, numerical solutions of the secondorder twodimensional sinegordon equation obtained by polynomial differential quadrature method have been discussed.
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