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A robust septic hermite collocation technique for dirichlet boundary condition Heat conduction equation Cover

A robust septic hermite collocation technique for dirichlet boundary condition Heat conduction equation

International Journal of Mathematics and Computer in Engineering
Volume 3 (2025): Issue 2 (December 2025)
By: Selçuk Kutluay,  Nuri Murat Yağmurlu and  Ali Sercan Karakaş  
Open Access
|Sep 2024

Figures & Tables

A comparison of the computed error norm L∞ of the proposed scheme with those given in [7, 11, 12] for various values of h = k at T = 1_

h = kSHCM-LSHCM-C[7][12] (CN)[12] (CBVM)[11] CHCM-L
0.25.1578 × 10−55.1552 × 10−51.4145 × 10−11.1 × 10−12.8 × 10−25.8498 × 10−5
0.13.1586 × 10−53.1587 × 10−53.7195 × 10−23.0 × 10−23.8 × 10−33.1584 × 10−5
0.059.7106 × 10−69.7107 × 10−68.4588 × 10−36.9 × 10−32.7 × 10−49.7065 × 10−6
0.0252.5489 × 10−62.5489 × 10−62.0698 × 10−31.7 × 10−31.3 × 10−52.5485 × 10−6
0.01256.4490 × 10−76.4490 × 10−75.1473 × 10−44.2 × 10−45.1 × 10−76.4488 × 10−7
0.006251.6171 × 10−71.6171 × 10−7 1.1 × 10−43.6 × 10−81.6171 × 10−7
0.014.1333 × 10−74.1333 × 10−7 4.1332 × 10−7
0.0051.0353 × 10−71.0353 × 10−7 1.0353 × 10−7
0.00252.5895 × 10−82.5895 × 10−8 2.5895 × 10−8
0.0021.6574 × 10−81.6574 × 10−8 1.6574 × 10−8
0.0014.1437 × 10−94.1437 × 10−9 4.1437 × 10−9

A comparison of the computed error norm L2 of the proposed scheme with those given in [11, 15] for M = 10, 20, 40 and k = 1/106 at T = 0_1_

hSHCM-L[15][15][11] CHCM-L
θ = 0.1θ = 0.2
1/106.2482 × 10−131.6534 × 10−42.4968 × 10−41.6957 × 10−6
1/203.3280 × 10−124.3906 × 10−77.8152 × 10−71.0426 × 10−7
1/405.8595 × 10−128.6154 × 10−108.0111 × 10−106.4916 × 10−9
θ = 0.3θ = 0.4
1/106.2482 × 10−133.2357 × 10−43.6276 × 10−41.6957 × 10−6
1/203.3280 × 10−121.0791 × 10−61.2556 × 10−61.0426 × 10−7
1/405.8595 × 10−129.2171 × 10−101.1166 × 10−96.4916 × 10−9
θ = 0.5θ = 0.6
1/106.2482 × 10−133.5225 × 10−42.8316 × 10−41.6957 × 10−6
1/203.3280 × 10−121.2494 × 10−61.0109 × 10−61.0426 × 10−7
1/405.8595 × 10−121.2167 × 10−91.1107 × 10−96.4916 × 10−9
θ = 0.7θ = 0.8
1/106.2482 × 10−131.5954 × 10−41.9640 × 10−41.6957 × 10−6
1/203.3280 × 10−125.4419 × 10−79.1503 × 10−71.0426 × 10−7
1/405.8595 × 10−127.4804 × 10−108.6751 × 10−106.4916 × 10−9
θ = 0.9θ = 0.95
1/106.2482 × 10−134.5197 × 10−46.1645 × 10−41.6957 × 10−6
1/203.3280 × 10−122.0820 × 10−62.8818 × 10−61.0426 × 10−7
1/405.8595 × 10−122.4668 × 10−93.6858 × 10−96.4916 × 10−9

A comparison of the computed error norms L2 and L∞ of the proposed scheme with those given in [9, 11] for h = 1/16, k = 0_01 at various T_

tfinalL2L∞
SHCM-L[11] CHCM-L[9]SHCM-L[11] CHCM-L[9]
0.15.1774 × 10−42.9917 × 10−44.86 × 10−32.9891 × 10−42.9891 × 10−46.79 × 10−3
0.32.1558 × 10−41.2457 × 10−48.87 × 10−51.2447 × 10−41.2447 × 10−43.76 × 10−4
0.54.9872 × 10−52.8818 × 10−51.73 × 10−32.8793 × 10−52.8793 × 10−52.44 × 10−4
0.79.6911 × 10−65.5999 × 10−62.04 × 10−45.5950 × 10−65.5953 × 10−63.17 × 10−4
0.91.7294 × 10−69.9934 × 10−72.14 × 10−39.9847 × 10−79.9856 × 10−73.14 × 10−3
1.07.1591 × 10−74.1368 × 10−72.15 × 10−34.1332 × 10−74.1338 × 10−73.32 × 10−3

A comparison of the computed error norm L2 by the proposed scheme with those given in [11, 15] for h = 1/1000 and k = 0_01, 0_005, 0_0025 at T = 1_

kSHCM-LSHCM-C[15][11]CHCM-L
0.017.1591 × 10−77.1591 × 10−74.2273 × 10−44.1333 × 10−7
0.0051.7931 × 10−71.7932 × 10−71.0560 × 10−41.0353 × 10−7
0.00254.4851 × 10−84.4851 × 10−82.6395 × 10−52.5895 × 10−8

A comparison of the computed error norm L2 of the proposed scheme with those given in [10, 11] for M = 5, 10, 20 and k = 1/106 at T = 1_

hSHCM-LSHCM-C[10] (CN-I)[10] (CN-II)[11] CHCM-L
1/51.2153 × 10−141.0075 × 10−124.7696 × 10−68.5859 × 10−33.5716 × 10−8
1/101.9449 × 10−152.3323 × 10−147.7143 × 10−92.1412 × 10−32.2848 × 10−9
1/204.6215 × 10−157.4211 × 10−151.8820 × 10−115.3498 × 10−41.4361 × 10−10
1/408.1433 × 10−159.6794 × 10−15
DOI: https://doi.org/10.2478/ijmce-2025-0019 | Journal eISSN: 2956-7068
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Language: English
Page range: 253 - 266
Submitted on: Feb 23, 2024
Accepted on: May 11, 2024
Published on: Sep 19, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
1D Heat equation,
approximate solutions,
septic hermite collocation method,
finite elements method,
stability analysis
Related subjects:
Computer sciences,
Computer sciences, other,
Engineering,
Introductions and overviews,
Engineering, other,
Mathematics,
General mathematics,
Physics,
Physics, other

© 2024 Selçuk Kutluay, Nuri Murat Yağmurlu, Ali Sercan Karakaş, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

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