On an m-point boundary-value problem for second-order ordinary differential equations
Nonlinear Analysis: Theory, Methods & Applications
On an M-point boundary value problem
Nonlinear Analysis: Theory, Methods & Applications
Positive solutions for second-order m-point boundary value problems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Upper and lower solution method for fourth-order four-point boundary value problems
Journal of Computational and Applied Mathematics
The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems
Applied Numerical Mathematics
A fourth-order compact finite difference method for higher-order Lidstone boundary value problems
Computers & Mathematics with Applications
Upper and lower solution method for fourth-order four-point boundary value problems
Journal of Computational and Applied Mathematics
On 2nth-order nonlinear multi-point boundary value problems
Mathematical and Computer Modelling: An International Journal
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A fourth-order compact finite difference method is proposed for a class of nonlinear 2nth-order multi-point boundary value problems. The multi-point boundary condition under consideration includes various commonly discussed boundary conditions, such as the three- or four-point boundary condition, (n+2)-point boundary condition and 2(n-m)-point boundary condition. The existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. The convergence and the fourth-order accuracy of the method are proved. An efficient monotone iterative algorithm is developed for solving the resulting nonlinear finite difference systems. Various sufficient conditions for the construction of upper and lower solutions are obtained. Some applications and numerical results are given to demonstrate the high efficiency and advantages of this new approach.