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Approximate solution of complex differential equations for a rectangular domain with Taylor collocation method. (English) Zbl 1096.65075
Summary: A Taylor collocation method is investigated for the approximate computation of high-order linear complex differential equations. Using the collocation points on any rectangular domain in the complex plane, the method transforms the given complex differential equation and the mixed conditions to matrix equation with unknown Taylor coefficients. By means of the obtained matrix equations, the Taylor coefficients can be easily computed. Hence, the finite Taylor series approach is obtained. Also, examples are presented and the results are discussed.
MSC:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65E05Numerical methods in complex analysis
34M25Formal solutions, transform techniques (ODE in the complex domain)
65L05Initial value problems for ODE (numerical methods)