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Zbl 1221.65177
Wang, Yulan; Cao, Xuejun; Li, Xiaona
A new method for solving singular fourth-order boundary value problems with mixed boundary conditions. (English)
[J] Appl. Math. Comput. 217, No. 18, 7385-7390 (2011). ISSN 0096-3003

For the class of singular fourth order differential equations of the form $$u^{4}(x)+ \sum^{4}_{i=1}\frac{p_{i}(x)u^{(i-1)}(x)}{x^{\alpha_{i}}(1-x)^{\beta_{i}}}=f(x), \quad x\in (0,1)$$ with mixed boundary conditions is constructed an algorithm giving its analytical exact solution. This solution is obtained using the Gram-Schmidt orthonormalization process of special functions $\psi_{i}(x)$ and set of points ${x_{i}}$ dense in $[0,1]$
[Ivan Secrieru (Chişinău)]

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
65L60 Finite numerical methods for ODE
34B05 Linear boundary value problems of ODE
65L70 Error bounds (numerical methods for ODE)

Keywords: mixed boundary value problems; reproducing kernel Hilbert space; singular-coefficient; collocation method; error estimation; fourth order; Gram-Schmidt orthonormalization

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Zentralblatt MATH Berlin [Germany]