Solving Higher-Order Boundary and Initial Value Problems via Chebyshev–Spectral Method: Application in Elastic Foundation
Abstract
:1. Introduction
2. Some Preliminaries
3. Outline of the Method for Boundary and Initial Value Problems
3.1. Operational Matrix of Derivative
3.2. Description of the Proposed Method for BVPs and IVPs
Algorithm 1: The construction of proposed method for the boundary value problems (BVPs) |
Step 1. Input: ; ; Step 2. Compute: ; for . Step 3. Compute the matrix from matrix . Step 4. Compute: 4.1. from step 3, (i=2, …, n). 4.2. based on from (22). Step 5. Set: Step 6. Obtain the solution from the system of (24) and set: . |
Construction of the Proposed Method for IVPs
4. Numerical Results
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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N | Maximal Errors |
---|---|
Presented Method | |
7 | |
8 | |
10 | |
12 | |
15 |
N | Maximal Errors | ||
---|---|---|---|
Presented Method | Method in [3] | Method in [9] | |
6 | |||
8 | |||
11 | |||
15 | |||
18 |
N | Maximal Errors | |
---|---|---|
Exp. 3 | Exp. 4 | |
11 | ||
13 | ||
15 | ||
17 |
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Agarwal, P.; Attary, M.; Maghasedi, M.; Kumam, P. Solving Higher-Order Boundary and Initial Value Problems via Chebyshev–Spectral Method: Application in Elastic Foundation. Symmetry 2020, 12, 987. https://doi.org/10.3390/sym12060987
Agarwal P, Attary M, Maghasedi M, Kumam P. Solving Higher-Order Boundary and Initial Value Problems via Chebyshev–Spectral Method: Application in Elastic Foundation. Symmetry. 2020; 12(6):987. https://doi.org/10.3390/sym12060987
Chicago/Turabian StyleAgarwal, Praveen, Maryam Attary, Mohammad Maghasedi, and Poom Kumam. 2020. "Solving Higher-Order Boundary and Initial Value Problems via Chebyshev–Spectral Method: Application in Elastic Foundation" Symmetry 12, no. 6: 987. https://doi.org/10.3390/sym12060987