An integral-like numerical approach for solving Burgers' equation

An integral-like approach established on spline polynomial interpolations is applied to the one-dimensional Burgers' equation. The Hopf-Cole transformation that converts non-linear Burgers' equation to linear diffusion problem is emulated by using Taylor series expansion. The diffusion equation is then solved by using analytic integral formulas. Four experiments were performed to examine its accuracy, stability and parallel scalability. The correctness of the numerical solutions is evaluated by comparing with exact solution and assessed error norms. Due to its integral-like characteristic, large time step size can be employed without loss of accuracy and numerical stability. For practical applications, at least cubic interpolation is recommended. Parallel efficiency seen in the weak-scaling experiment depends on time step size but generally adequate.