A spectral regularization method for a Cauchy problem of the modified Helmholtz equation.(English)Zbl 1198.65114

Summary: We consider the Cauchy problem for a modified Helmholtz equation, where the Cauchy data is given at $$x=1$$ and the solution is sought in the interval $$0<x<1$$. A spectral method together with the choice of the regularization parameter is presented and an error estimate is obtained. Combining the method of lines, we formulate regularized solutions which are stably convergent to the exact solutions.

MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A30 Linear ordinary differential equations and systems 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L70 Error bounds for numerical methods for ordinary differential equations
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References:

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