A hybrid B-spline collocation technique for the Caputo time fractional nonlinear Burgers’ equation

Abstract

Background This study proposes an efficient and stable technique based on new hybrid B-spline (HB-spline) functions for the numerical treatment of the Caputo time fractional nonlinear Burgers’ (TFNB) equation. The time derivative is discretized using the definition of the Caputo derivative, whereas HB-spline functions are used to discretize the spatial derivatives. The Rubin–Graves technique is used to linearize the nonlinear terms. Results The performance and efficacy of the established method are tested using three examples. The graphical results represent the smoothness between numerical and exact solutions. The absolute errors are very low as $$1{0}^{-4}$$ 1 0 - 4 and $$1{0}^{-5}$$ 1 0 - 5 . The convergence rate shows that the proposed method is second-order accurate in space. Conclusions The proposed method provides better results than the methods available in the literature. The method yields highly accurate results and can handle large-scale problems, which is the novelty of the present work.

Redefined Quintic B-Spline Collocation Method to Solve the Time-Fractional Whitham-Broer-Kaup Equations

“…The collocation method is widely used to obtain solutions for partial differential equations [24][25][26][27]. Depending on the situation, it can be useful to find the solution of fractional partial differential equations (FPDEs) at various locations within the given problem domain.…”