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Collocation method and residual correction using Chebyshev series. (English) Zbl 1090.65096
Summary: The Chebyshev collocation method is proposed to solve the linear two-point boundary value problems. Correction of the approximated solution is obtained using the residual function of the operator equation. The error differential equation, obtained by residual function, is solved by a truncated Chebyshev series (TCS), where the order of the TCS is bigger than the order of the TCS in the Chebyshev collocation method. The obtained approximate solution for the collocation method is corrected by the error differential equation.
MSC:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B05Linear boundary value problems for ODE
65L10Boundary value problems for ODE (numerical methods)
65L70Error bounds (numerical methods for ODE)