## A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems.(English)Zbl 0983.65090

Summary: We propose an algorithm for solving the nonliner two-point boundary value problem $u''(x)+\lambda F(x,u(x))= 0,\quad 0< x< 1,\quad u(0)= u(1)= 0,$ that has at least one positive solution for $$\lambda$$ in a compatible interval. Our method stems mainly from combining the decomposition series solution obtained by Adomian decomposition method with Padé approximates. The validity of the approach is verified through illustrative numerical examples.

### MSC:

 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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