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Displaying similar documents to “Computationally efficient technique for solving ODE systems exhibiting initial and boundary layers.”

The existence of a solution and a numerical method for the Timoshenko nonlinear wave system

Jemal Peradze (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by...

Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods

Kamel Al-Khaled (2014)

Applications of Mathematics

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This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate...