TY - JOUR
ID - 43684
TI - A generalized form of the parametric spline methods of degree (2k + 1) for solving a variety of two-point boundary value problems
JO - Iranian Journal of Numerical Analysis and Optimization
JA - IJNAO
LA - en
SN - 2423-6977
AU - Sarvari, Z.
AD - Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Y1 - 2023
PY - 2023
VL - 13
IS - Issue 4
SP - 578
EP - 603
KW - Boundary value problems
KW - Parametric spline
KW - Band matrices
KW - Pascalâ€™s triangle
DO - 10.22067/ijnao.2023.79288.1192
N2 - In this paper, a high order accuracy method is developed for finding the approximate solution of two-point boundary value problems. The present approach is based on a special algorithm, taken from Pascalâ€™s triangle, for obtaining a generalized form of the parametric splines of degree (2k + 1), k = 1, 2, . . . , which has a lower computational cost and gives the better ap-proximation. Some appropriate band matrices are used to obtain a matrix form for this algorithm.The approximate solution converges to the exact solution of order O(h4k ), where k is a quantity related to the degree of parametric splines and the number of matrix bands that are applied in this paper. Some examples are given to illustrate the applicability of the method, and we compare the computed results with other existing known methods. It isobserved that our approach produced better results.
UR - https://ijnao.um.ac.ir/article_43684.html
L1 - https://ijnao.um.ac.ir/article_43684_5df402f8cb2364e5eee61b0e658bb547.pdf
ER -