A New Numerical Algorithm for Two-Point Boundary Value Problems
Lihua Guo,Boying Wu,Dazhi Zhang +2 more
TL;DR: In this paper, a new numerical algorithm for two-point boundary value problems is presented, which first presents the exact solution in the form of series and then proves that the n-term numerical solution converges uniformly to the same exact solution.
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Abstract: We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that the n-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.
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References
Theory of Reproducing Kernels.
TL;DR: In this paper, a short historical introduction is given to indicate the different manners in which these kernels have been used by various investigators and discuss the more important trends of the application of these kernels without attempting, however, a complete bibliography of the subject matter.
Solving singular boundary-value problems of higher even-order
Huanmin Yao,Yingzhen Lin +1 more
TL;DR: In this paper, a new algorithm for singular boundary-value problems of higher even-order based on the theory of numerical analysis in the reproducing kernel space has been proposed, which is a special case of the singular boundary value problem of higher order.
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Approximate Solution of Nonlinear Multi-Point Boundary Value Problem on the Half-Line
TL;DR: A novel weighted reproducingkernel space is constructed and the expression of reproducing kernel function skillfully is given and an efficient algorithm is provided to solve the nonlinear multi-point boundary value problem on the half-line.
Higher order method for singular boundary-value problems by using spline function
TL;DR: The construction of a spline function for a class of singular two-point boundary-value problems and it is shown to be order-h4 convergent for all α ∈ (0, 1).
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A non-uniform mesh finite difference method and its convergence for a class of singular two-point boundary value problems
Manoj Kumar,Tariq Aziz +1 more
TL;DR: The construction of second-order three-point finite difference method based on non-uniform mesh for a class of singular two-point boundary value (BV) problem is discussed and its second- order convergence for various α ∈ (0, 1).
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