A Chebyshev spectral integration method with deferred correction time stepping for viscoelastic dynamics with capillarity

A Chebyshev pseudospectral method for simulating second order in time and fourth order in space semilinear initial boundary value problems is introduced. The method uses deferred corrections to obtain fourth order accuracy in time and a spectral integration method which gives sparse matrices and overcomes the numerical instability associated with large Chebyshev differentiation matrices. The method is used to obtain results for some one and two dimensional problems.