A new shifted generalized Chebyshev approach for multi-dimensional sinh-Gordon equation

Abstract

This paper is devoted to the numerical treatment of multi-dimensional non-linear sinh-Gordon
equations. The (1+1) and (2+1) sinh-Gordon equations are numerically solved using two collocation
algorithms. The set of basis functions is selected as a set of generalized Chebyshev polynomials
(CPs) that are expressed as an orthogonal combinations of CPs. Some formulas related to these
polynomials are developed and utilized to propose our numerical algorithms. The two collocation
algorithms are followed to convert the sinh-Gordon equations into systems of non-linear equations
that can be handled with any suitable solver. Some examples accompanied by comparisons are
given to validate the efficiency of our presented algorithms.