Lucas and Fibonacci polynomials based approach for the study of one- and
two-dimensional Burger and heat-type equations
Abstract
In this work a numerical technique, combination of Lucas and Fibonacci
polynomials, is proposed for the solution of one- and two-dimensional
nonlinear heat type equations. In first round, for discretization,
finite difference has been used for time and Crank Nicolson scheme for
spatial part. In second round, the unknown functions have been
approximated by Lucas polynomial while their derivatives by Fibonacci
polynomials. With the help of these approximations, the nonlinear
partial differential equation transforms to a system of algebraic
equations which can be solved easily. Convergence of the method has been
investigated numerically. Performance of the method has been studied by
taking one- and two-dimensional heat and burger equations. Efficiency of
the technique has been investigated in terms of root mean square (RMS),
L2 and L_infnty norms. The obtained results are then compared with
those available in the literature.