Abstract
The numerical method proposed by Whitam and Fornberg and developed by the authors for Cauchy-type problems in non-linear wave theory, is generalized to initial boundary-value problems. Differing from previous papers where the solution was approximated by Fourier series, Chebyshev polynomials are chosen as the basis functions. It is shown that in this case the effectiveness of the method is also preserved when boundary conditions exist. The conclusions are underlined by calculations on well-known examples — initial boundary-value problems for Burgers' equation and the heat conduction equation. A comparison with results obtained by finite-difference methods is carried out.
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