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Euler's Method Approximation

Given an initial value ( y(x_0) = y_0 ), Euler's method approximates the solution of the ODE by stepping forward in small increments. Consider the ODE: [ \frac{dy}{dx} = x + y ] with the initial ...
JSTOR Daily

Numerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type

Abstract. Numerical approximations to the solution of a linear singularly perturbed parabolic convection-diffusion problem are generated using a backward Euler method in time and an upwinded finite ...
IEEE

Numerical solution of 2D Euler equations for the transonic flow past over NACA0012 and RAE2822 airfoils using high order accurate Runge-Kutta Discontinuous Galerkin method

Abstract: The Runge-Kutta Discontinuous Galerkin (RKDG) finite element method has the several advantages. First, the method is better suited than finite difference methods to handle complicated ...
Scientific Research Publishing

Li, R.H. and Liu, B. (2009) Numerical Solution of Differential Equation. Higher Education Press, Beijing.

ABSTRACT: In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to ...