Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines
Anomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the tim...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
|
| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/29/6/100 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846103810519334912 |
|---|---|
| author | Priyanka Priyanka Shelly Arora Saroj Sahani Sharandeep Singh |
| author_facet | Priyanka Priyanka Shelly Arora Saroj Sahani Sharandeep Singh |
| author_sort | Priyanka Priyanka |
| collection | DOAJ |
| description | Anomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the time variable using an L1 finite-difference scheme and space discretization using the quintic Hermite spline collocation method. The hybrid technique reduces the problem to an iterative scheme of an algebraic system of equations. The stability analysis of the proposed numerical scheme and the optimal error bounds for the approximate solution are also studied. A comparative study of the obtained results and an error analysis of approximation show the efficiency, accuracy, and effectiveness of the technique. |
| format | Article |
| id | doaj-art-b1a9a05bf12e473d80694d23010dc168 |
| institution | Kabale University |
| issn | 1300-686X 2297-8747 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj-art-b1a9a05bf12e473d80694d23010dc1682024-12-27T14:38:24ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472024-11-0129610010.3390/mca29060100Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite SplinesPriyanka Priyanka0Shelly Arora1Saroj Sahani2Sharandeep Singh3Department of Mathematics, Punjabi University, Patiala 147002, IndiaDepartment of Mathematics, Punjabi University, Patiala 147002, IndiaDepartment of Mathematics, South Asian University, New Delhi 110068, IndiaDepartment of Mathematical and Statistical Sciences, Faculty of Science, University of Alberta, Edmonton, AB T6G2G1, CanadaAnomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the time variable using an L1 finite-difference scheme and space discretization using the quintic Hermite spline collocation method. The hybrid technique reduces the problem to an iterative scheme of an algebraic system of equations. The stability analysis of the proposed numerical scheme and the optimal error bounds for the approximate solution are also studied. A comparative study of the obtained results and an error analysis of approximation show the efficiency, accuracy, and effectiveness of the technique.https://www.mdpi.com/2297-8747/29/6/100multi-term fractional derivativeCaputo derivativeL1-schemequintic Hermite splinecollocation method |
| spellingShingle | Priyanka Priyanka Shelly Arora Saroj Sahani Sharandeep Singh Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines Mathematical and Computational Applications multi-term fractional derivative Caputo derivative L1-scheme quintic Hermite spline collocation method |
| title | Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines |
| title_full | Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines |
| title_fullStr | Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines |
| title_full_unstemmed | Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines |
| title_short | Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines |
| title_sort | numerical study of multi term time fractional sub diffusion equation using hybrid l1 scheme with quintic hermite splines |
| topic | multi-term fractional derivative Caputo derivative L1-scheme quintic Hermite spline collocation method |
| url | https://www.mdpi.com/2297-8747/29/6/100 |
| work_keys_str_mv | AT priyankapriyanka numericalstudyofmultitermtimefractionalsubdiffusionequationusinghybridl1schemewithquintichermitesplines AT shellyarora numericalstudyofmultitermtimefractionalsubdiffusionequationusinghybridl1schemewithquintichermitesplines AT sarojsahani numericalstudyofmultitermtimefractionalsubdiffusionequationusinghybridl1schemewithquintichermitesplines AT sharandeepsingh numericalstudyofmultitermtimefractionalsubdiffusionequationusinghybridl1schemewithquintichermitesplines |