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An O(h 4 ) accurate cubic spline TAGE method for nonlinear singular two point boundary value problems. (English) Zbl 1060.65080
Summary: We propose two parameter alternating group explicit (TAGE) method for the numerical solution of u '' +α ru ' -α 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:
65L10Boundary value problems for ODE (numerical methods)
65L70Error bounds (numerical methods for ODE)
34B16Singular nonlinear boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE