Solution of nonlinear initial-boundary value problems by sinc collocation-interpolation methods.

*(English)*Zbl 0822.65075The authors present the solution of initial-boundary value problems for nonlinear equations in one and two space dimensions. In order to obtain the solution collocation-interpolation methods are applied which use sinc functions. These functions are used to interpolate dependent variables in space or time. Then technical calculations recover the evaluation of the dependent variables in the collocation points in terms of a set of ordinary differential equations.

It appears that if the sinc interpolation is in space then the ordinary derivative is obtained with respect to time, and if the interpolation is in time then the ordinary derivative is obtained with respect to space. The authors show an application of the method developed to the solution of a nonlinear problem in hydrodynamics. The analysis of convergence and some research perspectives are also presented.

It appears that if the sinc interpolation is in space then the ordinary derivative is obtained with respect to time, and if the interpolation is in time then the ordinary derivative is obtained with respect to space. The authors show an application of the method developed to the solution of a nonlinear problem in hydrodynamics. The analysis of convergence and some research perspectives are also presented.

Reviewer: A.Marciniak (Poznań)

##### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

35G10 | Initial value problems for linear higher-order PDEs |

35K25 | Higher-order parabolic equations |

##### Keywords:

nonlinear initial-boundary value problems; evolution equations; collocation-interpolation methods; sinc functions; convergence
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\textit{N. Bellomo} and \textit{L. Ridolfi}, Comput. Math. Appl. 29, No. 4, 15--28 (1995; Zbl 0822.65075)

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