Numerical solution of the Burgers’ equation by automatic differentiation. (English) Zbl 1193.65154

Asaithambi, Asai

Appl. Math. Comput. 216, No. 9, 2700-2708 (2010).

Summary: We compute the solution of the one-dimensional Burgers’ equation by marching the solution in time using a Taylor series expansion. Our approach does not require symbolic manipulation and does not involve the solution of a system of linear or non-linear algebraic equations. Instead, we use recursive formulas obtained from the differential equation to calculate exact values of the derivatives needed in the Taylor series. We illustrate the effectiveness of our method by solving four test problems with known exact solutions. The numerical solutions we obtain are in excellent agreement with the exact solutions, while being superior to other previously reported numerical solutions.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q53	KdV equations (Korteweg-de Vries equations)
68W30	Symbolic computation and algebraic computation
65D25	Numerical differentiation

Keywords:

Burgers’ equation; Taylor series; automatic differentiation; recursive evaluation of derivatives; numerical examples; finite difference method

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