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A new method for solving singular fourth-order boundary value problems with mixed boundary conditions. (English) Zbl 1221.65177

For the class of singular fourth order differential equations of the form

${u}^{4}\left(x\right)+\sum _{i=1}^{4}\frac{{p}_{i}\left(x\right){u}^{\left(i-1\right)}\left(x\right)}{{x}^{{\alpha }_{i}}{\left(1-x\right)}^{{\beta }_{i}}}=f\left(x\right),\phantom{\rule{1.em}{0ex}}x\in \left(0,1\right)$

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 ${\psi }_{i}\left(x\right)$ and set of points ${x}_{i}$ dense in $\left[0,1\right]$

##### MSC:
 65L10 Boundary value problems for ODE (numerical methods) 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE 34B05 Linear boundary value problems for ODE 65L70 Error bounds (numerical methods for ODE)
##### References:
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