Second order linear O.D.E. and Riccati equations |
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| Authors: | Charles N Friedman |
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| Institution: | Department of Mathematics, The University of Texas, Austin, Texas 78712 U.S.A. |
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| Abstract: | We prove that approximate solutions of the Riccati equation ?′ + ?2 = a(x) yield asymptotic solutions y = e∝x?(s)ds of the second order linear equation y″ = a(x)y. We show that the iterative scheme ?0 = a, ?n + 12 = a ? ?n′ leads to asymptotic solutions of the cited linear equation in many interesting cases. |
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