Abstract
In this paper, the meshless method is employed for the numerical solution of the one-dimensional (1D) convection-diffusion equation based on radical basis functions (RBFs). Coupled with the time discretization and the collocation method, the proposed method is a truly meshless method which requires neither domain nor boundary discretization. The algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme
Highlights
Whenever we consider mass transport of a dissolved species or a component in a gas mixture, concentration gradients will cause diffusion
We present a numerical scheme to solve the convection-diffusion equation using the collocation method with Radial Basis Function (RBF)
The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme
Summary
Whenever we consider mass transport of a dissolved species (solute species) or a component in a gas mixture, concentration gradients will cause diffusion. The general convection-diffusion equation has the following form [2,3]: (1D) convection-diffusion equation: ut (x,t) + α ux (x,t) + β u(x,t) = ε uxx + f(x,t), a ≤ x ≤ b, 0 ≤ t, With the initial conditions: (1.1)
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