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A note on numerical solution of classical Darboux problem. (English) Zbl 1478.65097

Summary: Recently, many authors studied the numerical solution of the classical Darboux problem in its integral form via two-dimensional nonlinear Volterra-Fredholm integral equation. In the present article, a numerical technique based on the Chebyshev wavelet is proposed to solve the Darboux problem directly without converting into a nonlinear Volterra-Fredholm integral equation. The proposed technique is different from the techniques discussed in the literature. The proposed approach produces higher accuracy than its counterpart techniques. The proposed scheme is illustrated with suitable examples to show the advantages in terms of its accuracy with a lesser grid size.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65T60 Numerical methods for wavelets
41A50 Best approximation, Chebyshev systems
35L10 Second-order hyperbolic equations
35Q05 Euler-Poisson-Darboux equations
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