Boundary Complexity and Kernel Functions in Classical and Variational Concepts of Solving Geodetic Boundary Value Problems

2018 ◽  
pp. 31-41 ◽  
Author(s):  
Petr Holota ◽  
Otakar Nesvadba
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Kernel Functions ◽  
Geodetic Boundary ◽  
Boundary Complexity

Uniquely and overdetermined geodetic boundary value problems by least squares

1989 ◽  
Vol 63 (1) ◽  
pp. 1-33 ◽  
Author(s):  
R. Rummel ◽  
P. Teunissen ◽  
M. Gelderen
Keyword(s):  
Least Squares ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Geodetic Boundary

scholarly journals Reproducing Kernel Algorithm for the Analytical-Numerical Solutions of Nonlinear Systems of Singular Periodic Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Omar Abu Arqub
Keyword(s):  
Nonlinear Systems ◽  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Periodic Boundary ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Singular Systems ◽  
Boundary Value ◽  
Kernel Functions ◽  
Periodic Boundary Value Problems

The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order periodic boundary value problems with finitely many singularities. The analytical-numerical solutions are obtained in the form of an infinite convergent series for appropriate periodic boundary conditions in the spaceW230,1, whilst two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. The main characteristic feature of the utilized algorithm is that the global approximation can be established on the whole solution domain, in contrast with other numerical methods like onestep and multistep methods, and the convergence is uniform. Two numerical experiments are carried out to verify the mathematical results, whereas the theoretical statements for the solutions are supported by the results of numerical experiments. Our results reveal that the present algorithm is a very effective and straightforward way of formulating the analytical-numerical solutions for such nonlinear periodic singular systems.

scholarly journals Computational optimization in solving the geodetic boundary value problems

2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Marek Macák ◽  
◽  
Róbert Čunderlík ◽  
Karol Mikula ◽  
Zuzana Minarechová
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Computational Optimization ◽  
Geodetic Boundary
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