TY - JOUR
ID - 154716
TI - Orthogonal spline collocation methods for 1D-parabolic problems with interfaces
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Bhal, Santosh Kumar
AU - Behura, Snehalata
AU - Nandi, Ashish Kumar
AD - Department of Mathematics, School of Applied Sciences, Centurion University of Technology and Management, Paralakhemundi, India
AD - Department of Mathematics, CIPET:IPT, Bhubaneswar-751024, India.
AD - Mathematics Division, School of Advanced Sciences, Vellore Institute of Technology, Chennai, 600127, Tamil Nadu, India.
Y1 - 2022
PY - 2022
VL - 8
IS - 2
SP - 243
EP - 260
KW - Heat conduction equation
KW - Orthogonal cubic spline collocation methods
KW - Discontinuous data
KW - Cubic monomial basis functions
KW - Almost block diagonal (ABD) matrix
DO - 10.22034/kjm.2022.286589.2263
N2 - Orthogonal spline collocation methods (OSC) are used to solve one dimensional heat conduction problems with interfaces. Cubic monomial basis functions are used to approximate the solution for spatial discretization and the Crank-Nicolson method for time stepping. Existence and uniqueness results are established for a discrete problem. This method is easily extended to monomials of higher degree. We present the results of experiments involving several examples which show the efficiency of OSC method. For both cubic and quartic basis functions, the results of numerical experiments demonstrate fourth-order accuracy in L∞ and L2 norms, and third-order accuracy in theH1 norm. Moreover, sixth order superconvergence in nodal error of derivative of the OSC approximation for quartics is observed. OSC approach gives rise to almost block diagonal linear systems which are solved using standard software.
UR - https://www.kjm-math.org/article_154716.html
L1 - https://www.kjm-math.org/article_154716_53417164f62805e6f80372cfaf7fd20d.pdf
ER -