About a numerical method of successive interpolations for two-point boundary value problems with deviating argument

2011 ◽  
Vol 217 (19) ◽  
pp. 7772-7789 ◽  
Author(s):  
A.M. Bica ◽  
M. Curila ◽  
S. Curila
Keyword(s):  
Boundary Value Problems ◽  
Numerical Method ◽  
Boundary Value ◽  
Point Boundary ◽  
Deviating Argument

scholarly journals Improved error estimate and applications of the complete quartic spline

2019 ◽  
Vol 27 (2) ◽  
pp. 71-83
Author(s):  
Alexandru Mihai Bica ◽  
Diana Curilă ◽  
Zoltan Satmari
Keyword(s):  
Error Estimate ◽  
Boundary Value Problems ◽  
Numerical Method ◽  
Numerical Integration ◽  
Error Bound ◽  
Fourth Order ◽  
Boundary Value ◽  
Continuous Functions ◽  
Point Boundary ◽  
Lipschitzian Functions

AbstractIn this paper an improved error bound is obtained for the complete quartic spline with deficiency 2, in the less smooth class of continuous functions. In the case of Lipschitzian functions, the obtained estimate improves the constant from Theorem 3, in J. Approx. Theory 58 (1989) 58-67. Some applications of the complete quartic spline in the numerical integration and in the construction of an iterative numerical method for fourth order two-point boundary value problems with pantograph type delay are presented.

scholarly journals Iterative numerical method for fractional order two-point boundary value problems

2021 ◽  
Vol 38 (1) ◽  
pp. 47-55
Author(s):  
ALEXANDRU MIHAI BICA ◽  
Keyword(s):  
Differential Equations ◽  
Error Estimate ◽  
Boundary Value Problems ◽  
Numerical Method ◽  
Fractional Order ◽  
Boundary Value ◽  
Point Boundary ◽  
Boundary Problems ◽  
Numerical Example

In this paper we develop an iterative numerical method based on Bernstein splines for solving two-point boundary problems associated to differential equations of fractional order $\alpha\in\left( 0,1\right) $. The convergence of the method is proved by providing the error estimate and it is tested on a numerical example.

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