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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 (x)+ i=1 4 p i (x)u (i-1) (x) x α i (1-x) β i =f(x),x(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 ψ i (x) and set of points x i dense in [0,1]

MSC:
65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B05Linear boundary value problems for ODE
65L70Error bounds (numerical methods for ODE)
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