On the solution of Zabolotskaya–Khokhlov and Diffusion of Oxygen equations using a Sinc collocation method

Abstract

Recent progress seems to suggest that the use of Sinc collocation method for the numerical treatment of partial differential equations, as a great level of precision and accuracy has been obtained on computational grounds. Sinc functions based on collocation points, provide us, the approximation of functions over all types of problems containing singularities on semi-infinite domain as well as on boundaries. Two partial differential equations are tested by using cardinal expansion of Sinc functions. However, employing Sinc functions to reduce the governing PDEs into system of algebraic equations and using collocations points with matrix operations leads to desired results. Furthermore, this technique ensures higher accuracy and convergence of obtained results of numerical solutions.

Keywords

• Sinc collocation method
• Zabolotskaya–Khokhlov equation
• Diffusion of Oxygen equation
• Numerical solution
• Wave propagation
• Stability analysis