Abstract
This research paper represents a numerical approximation to non-linear coupled one dimension reaction diffusion system, which includes the existence and uniqueness of the time dependent solution with upper and lower bounds of the solution. Also numerical approximation is obtained by finite difference schemes to reach at reasonable level of accuracy, which is magnified by L2, L∞ and relative error norms. The accuracy of the approximations is shown by randomly selected grid points along time level and comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations with a little modifications.
Highlights
Numerical approximation is obtained by finite difference schemes to reach at reasonable level of accuracy, which is magnified by L2, L∞ and relative error norms
The schemes can be applied to a wide class of higher dimension non-linear reaction diffusion equations with a little modifications
Consistency of CN From accuracy, we find principle part of the truncation error along with Equation (42)
Summary
Q ( ρ ) is a limited to originator term that illuminate the net rate of production or growth in the populated area or density associated to population [3]. The behaviour of the diffusion is accounted in the flux i, inclines by Fick’s law, i =−D∂xρ, (2). Where the assumption on the diffusion coefficient D, is to be constant [3]. It is frequently to imitate the law, which is known as the Pearl-Verhulst logistic law, Q(ρ) ⇒ γρ 1−
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