A Bivariate Spectral Linear Partition Method for Solving Nonlinear
Evolution Equations
Abstract
This work develops a method for solving nonlinear evolution
equations. The method, termed a bivariate spectral linear partition
method, BSLPM, combines the Chebyshev spectral collocation method,
bivariate Lagrange interpolation, and a linear partition technique as an
underlying linearization method. It is developed for an n th
order nonlinear differential equation and then used to solve
three known evolution problems. The results are compared with known
exact solutions from literature. The method’s applicability,
reliability, and accuracy are confirmed by the congruence between the
numerical and exact solutions. Tables, error graphs, and convergence
graphs were generated using MATLAB (R2015a), to confirm the order of
accuracy of the method and verify its convergence. The performance of
the method is also observed against other methods performing well in
these types of differential equations and is found to be comparable in
terms of accuracy. The proposed method is also efficient as it uses
minimal computation time.
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