Implementing a Numerical Solution of the KPI Equation Using Single Assignment C: Lessons and Experiences
نویسندگان
چکیده
We report our experiences of programming in the functional languageSaC[1] anumericalmethod for theKPI (Kadomtsev-Petiviashvili I)equation.KPIdescribesthepropagationofnonlinearwaves inadispersive medium. It is an integro-differential, nonlinear equation with third-order derivatives, and so it presents a noticeable challenge in numerical solution, as well as being an important model for a range of topics in computational physics.The latter include: long internalwaves inadensity-stratifiedocean, ion-acoustic waves in a plasma, acoustic waves on a crystal lattice, and more. Thus our solution of KPI in SaC represents an experience of solving a “real” problem using a single-assignment language and as such provides an insight into the kind of challenges and benefits that arise in using the functional paradigm in computational applications. The paper describes the structure and functionality of the program, discusses the features of functional programming that make it useful for the task in hand, and touches upon performance issues.
منابع مشابه
Numerical Solution of Caputo-Fabrizio Time Fractional Distributed Order Reaction-diffusion Equation via Quasi Wavelet based Numerical Method
In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...
متن کاملNumerical solution of fuzzy Hunter-Saxton equation by using Adomian decomposition and Homotopy analysis methods
In this paper, a fuzzy Hunter-Saxton equation is solved by using the Adomian'sdecomposition method (ADM) and homotopy analysis method (HAM). Theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. The existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. A numerical...
متن کاملNumerical Solution of Fractional Black Scholes Equation Based on Radial Basis Functions Method
Options pricing have an important role in risk control and risk management. Pricing discussion requires modelling process, solving methods and implementing the model by real data in a given market. In this paper we show a model for underlying asset based on fractional stochastic models which is a particular type of behavior of stochastic assets changing. In addition a numerical method based on ...
متن کاملNUMERICAL SOLUTION OF BOUSSINESQ EQUATION USING MODIFIED ADOMIAN DECOMPOSITION AND HOMOTOPY ANALYSIS METHODS
In this paper, a Boussinesq equation is solved by using the Adomian's decomposition method, modified Adomian's decomposition method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods ...
متن کاملNumerical solution of the one dimensional non-linear Burgers equation using the Adomian decomposition method and the comparison between the modified Local Crank-Nicolson method and the VIM exact solution
The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to...
متن کامل