The use of quadratures for solving convective and highly stiff transport problems

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Abstract

In this paper we introduce a method for the numerical solutions of initial value problems, that combines finite differences with Simpson’s rule. The effectiveness of the method is proved by solving, in one spatial dimension, a stiff and convection-dominated transport problem. To solve the same problem in two spatial dimensions, the proposed method was used successfully in combination with Strang’s operator decomposition method.

Keywords

Initial value problem
Time-stepping scheme
Operator splitting
Strang’s method
Convection–diffusion
Stiff problem

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