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Solution of nonlinear evolution problems by parallelized collocation-interpolation methods. (English) Zbl 0905.35046
Summary: This paper deals with the solution of initial-boundary value problems for nonlinear evolution equations. The solution technique is based on collocation-interpolation methods which are improved in order to reduce computational errors at fixed discretizations of the independent variables. The method consists in parallelizing the approximation of the space derivatives so that the same approximation is reached by a lower number of collocation points, and hence, by a lower computation time. The analysis includes a theoretical and computational estimate both of the approximation error and of the computational time.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
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