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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:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
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References:
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