Numerical study of 1D and 2D advection-diffusion-reaction equations using Lucas and Fibonacci polynomials
Numerical study of 1D and 2D advection-diffusion-reaction equations using Lucas and Fibonacci polynomials
Abstract In this work, a numerical scheme based on combined Lucas and Fibonacci polynomials is proposed for one- and two-dimensional nonlinear advection–diffusion–reaction equations. Initially, the given partial differential equation (PDE) reduces to discrete form using finite difference method and $$\theta -$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>θ</mml:mi><mml:mo>-</mml:mo></mml:mrow></mml:math> weighted scheme. Thereafter, the unknown functions have …