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Zbl 1060.65080
Mohanty, R.K.; Sachdev, P.L.; Jha, Navnit
An $O(h^4)$ accurate cubic spline TAGE method for nonlinear singular two point boundary value problems. (English)
[J] Appl. Math. Comput. 158, No. 3, 853-868 (2004). ISSN 0096-3003

Summary: We propose two parameter alternating group explicit (TAGE) method for the numerical solution of $u''+ {\alpha\over r} u'- {\alpha\over r^2} u= f(r)$, $0< r< 1$ using a fourth-order accurate cubic spline method with specified boundary conditions at the endpoints. The proof of convergence of the TAGE method when the coefficient matrix is unsymmetric and real is presented. We also discuss the Newton-TAGE method for the numerical solution of nonlinear singular two point boundary value problems using the cubic spline method with same accuracy of order four. Numerical results are provided to illustrate the viability of the proposed TAGE method.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
65L70 Error bounds (numerical methods for ODE)
34B16 Singular nonlinear boundary value problems
65L20 Stability of numerical methods for ODE

Keywords: TAGE method; Newton-TAGE method; convergence; two parameter alternating group explicit method; numerical results; cubic spline method; nonlinear singular two point boundary value problem

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Zentralblatt MATH Berlin [Germany]