Finite sine transform method
WebDec 4, 2005 · In this article we use the Fokas transform method to analyze boundary value prob-lems for the sine-Gordon equation posed on a finite interval. The representation of ... The sine-Gordon Equation on a Finite Interval 521 2 The linearized equation We consider the small q limit of the sine-Gordon equation, given by qxt +q = 0, x ∈ (0,L), t ∈ ... WebMar 15, 2024 · , A fast Sine transform accelerated high order finite difference method for parabolic problems over irregular domains, J. Sci. Comput. (2024) revised. Google Scholar [36] Li J., Melenk J.M., Wohlmuthc B., Zou J., Optimal a priori estimates for higher order finite elements for elliptic interface problems, Appl. Numer. Math. 60 (2010) 19 – 37.
Finite sine transform method
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WebNov 1, 2024 · An implicit finite difference method is employed to discretize the Riesz space fractional diffusion equations with a penalty term in a rectangular region by the volume-penalization approach. The stability and the convergence of the proposed method are studied. ... the generalized minimum residual method with a preconditioner based on the … WebSep 15, 2024 · Recently I came across finite Fourier transforms, which can be used for solving certain type of boundary value problem (BVP) of linear partial differential …
Using standard methods of numerical evaluation for Fourier integrals, such as Gaussian or tanh-sinh quadrature, is likely to lead to completely incorrect results, as the quadrature sum is (for most integrands of interest) highly ill-conditioned. Special numerical methods which exploit the structure of the oscillation are required, an example of which is Ooura's method for Fourier integrals This method attempts to evaluate the integrand at locations which asymptotically approach the zero… WebBoth of these transforms can be used to reduce a PDE to an ODE. Examples of the Sine Transform Consider the function f(x) = 1 on (0;1). If we apply the nite sine transform to this function, we obtain S n = 2 Z 1 0 sin(nˇx)dx = 2 nˇ cos(nˇx) 1 0 = ( 4 nˇ nodd 0 neven: Applying the inverse sine transform yields 1 = 4 ˇ X1 n=1 1 2n 1 sin[(2n ...
WebMay 1, 2016 · In this paper, based on fast discrete Sine transform, we design an efficient algorithm to implement this scheme. To do this, Poisson equation is first discretized by fourth-order compact finite difference method. The subsequent discretized system is not solved by the usual method—matrix inversion, instead it is solved with the fast discrete ... WebNov 1, 2024 · An implicit finite difference method is employed to discretize the Riesz space fractional diffusion equations with a penalty term in a rectangular region by the volume …
WebIn Section 2, by using the method of Laplace and Fourier transforms, the fundamental solution of Problem 1 is derived. In Section 3, ... So we inverse Laplace and finite Sine transform for to obtain 5. Conclusions. In this paper we have considered the time-fractional telegraph equation. The fundamental solution for the Cauchy problem in a whole ...
WebJul 9, 2024 · We will also show that we can use a finite sine transform to solve nonhomogeneous problems on finite intervals. Along the way we will identify several Green’s functions. Fourier Transform and the Heat Equation. We will first consider the … imaging for peptic ulcer diseaseWebMar 20, 2024 · The derivation of this paper is devoted to describing the operational properties of the finite Fourier transform method, with the purpose of acquiring a … imaging for penile painWebIn mathematics the finite Fourier transform may refer to either another name for discrete-time Fourier transform (DTFT) of a finite-length series. E.g., F.J.Harris (pp. 52–53) … list of french car brandshttp://mx.nthu.edu.tw/~rklee/files/PDE-heat-integral.pdf imaging for pets cincinnatiWebFeb 25, 2024 · Abstract and Figures. The method of modified finite sine transform (MFST) was introduced to solve fourth-order boundary value problems in structural mechanics. The analytical features and ... imaging for perilymphatic fistulaWebMar 26, 2024 · In this paper, a new Cartesian grid finite difference scheme is introduced for solving parabolic initial-boundary value problems involving irregular domains and Robin boundary condition in two and three dimensions. In spatial discretization, a ray-casting matched interface and boundary (MIB) method is utilized to enforce different types of … list of french artistsWebFormula (6) transforms into its Fourier transform, and (5) is the inverse transform. Related to this are the Fourier cosine transform (Sec. 11.8) (7) and the Fourier sine transform(Sec. 11.8) (8) . The discrete Fourier transform (DFT)and a practical method of computing it, called the fast Fourier transform (FFT), are discussed in Sec. 11.9. fˆ ... imaging for rectovaginal fistula