Fractal Fract, Vol. 5, Pages 165: Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method
Fractal and Fractional doi: 10.3390/fractalfract5040165
Maryam G. Alshehri
An efficient technique, called pseudo-Galerkin, is performed to approximate some types of linear/nonlinear BVPs. The core of the performance process is the two well-known weighted residual methods, collocation and Galerkin. A novel basis of functions, consisting of first derivatives of Chebyshev polynomials, has been used. Consequently, new operational matrices for derivatives of any integer order have been introduced. An error analysis is performed to ensure the convergence of the presented method. In addition, the accuracy and the efficiency are verified by solving BVPs examples, including real-life problems.
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