An efficient collocation method for a Caputo two-point boundary value problem
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0539-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0539-4 | ||
| 245 | 0 | 3 | |a An efficient collocation method for a Caputo two-point boundary value problem |h [Elektronische Daten] |c [Natalia Kopteva, Martin Stynes] |
| 520 | 3 | |a A two-point boundary value problem is considered on the interval $$[0,1]$$ [ 0 , 1 ] , where the leading term in the differential operator is a Caputo fractional-order derivative of order $$2-\delta $$ 2 - δ with $$0<\delta <1$$ 0 < δ < 1 . The problem is reformulated as a Volterra integral equation of the second kind in terms of the quantity $$u'(x)-u'(0)$$ u ′ ( x ) - u ′ ( 0 ) , where $$u$$ u is the solution of the original problem. A collocation method that uses piecewise polynomials of arbitrary order is developed and analysed for this Volterra problem; then by postprocessing an approximate solution $$u_h$$ u h of $$u$$ u is computed. Error bounds in the maximum norm are proved for $$u-u_h$$ u - u h and $$u'-u_h'$$ u ′ - u h ′ . Numerical results are presented to demonstrate the sharpness of these bounds. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Caputo fractional derivative |2 nationallicence | |
| 690 | 7 | |a Collocation method |2 nationallicence | |
| 690 | 7 | |a Boundary value problem |2 nationallicence | |
| 700 | 1 | |a Kopteva |D Natalia |u Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland |4 aut | |
| 700 | 1 | |a Stynes |D Martin |u Beijing Computational Science Research Center, Haidian District, Beijing, China |4 aut | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/4(2015-12-01), 1105-1123 |x 0006-3835 |q 55:4<1105 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0539-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0539-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Kopteva |D Natalia |u Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Stynes |D Martin |u Beijing Computational Science Research Center, Haidian District, Beijing, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/4(2015-12-01), 1105-1123 |x 0006-3835 |q 55:4<1105 |1 2015 |2 55 |o 10543 | ||