This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.
In this paper the Burger's_Fisher equation inone dimension has been solved by using three finite differences methods which are the explicit method, exponential method and DuFort_Frankel method After comparing the numerical results of those methods with the exact solution for the equation, there has been found an excellent approximation between exact solution and Numerical solutions for those methods, the DuFort_Frankel method was the best method in one dimension.
In this paper we solved the Kuramoto-Sivashinsky Equation numerically by finitedifference methods, using two different schemes which are the Fully Implicit scheme and Exponential finite difference scheme, because of the existence of the fourth derivative in the equation we suggested a treatment for the numerical solution of the two previous scheme by parting the mesh grid into five regions, the first region represents the first boundary condition, the second at the grid point x1, while the third represents the grid points x2,x3,…xn-2, the fourth represents the grid point xn-1and the fifth is the second boundary condition. We also, studied the numerical stability by Fourier (Von-Neumann) method for the two scheme which used in the solution on all mesh points to ensure the stability of the point which had been treated in the suggested style, we using two interval with two initial condition and the numerical results obtained by using these schemes are compare with Exact Solution of Equation Excellent approximate is found between the Exact Solution and numerical Solutions of these methods.
In this paper we used two numerical methods to investigate propagating heat solutions of PDEs. The explicit and Crank-Nicolson methods and the results show that Crank-Nicolson method is more accurate than the explicit method. As an illustration, we used the above method to an autocatalytic reaction diffusion equations involving two diffusing chemicals in one dimension. Keywords: Crank-Nicolson Method, explicit, autocatalytic reaction diffusion equations. انك كر طريقة -نيكولسون االنتشار ذاتي تفاعل لنظم البياتي يونس عباس منا عبدهللا سعد ع الرو امين محمد عبدالغفور ژ بياني الموصل/العراق والرياضيات/جامعة الحاسوب علوم كلية البحث: استالم تاريخ 15 / 1 / 2005 ت البحث: قبول اريخ 30 / 5 / 2005 الملخص
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