Elhassan, A., Rabia, A., Mohamed, H., Ali, M., Emam, M., Faisal, R., Mohamed, S., Atta, A. (2024). Chebyshev spectral method for the Bratu problem. test, 1(1), 23-34. doi: 10.21608/aash.2024.368286
Ahmed Abo Elhassan; Ahmed Rabia; Hamdy Mohamed; Mohamed Ali; Mohamed Emam; Rashad Faisal; Saif Elden Mohamed; Ahmed Gamal Atta. "Chebyshev spectral method for the Bratu problem". test, 1, 1, 2024, 23-34. doi: 10.21608/aash.2024.368286
Elhassan, A., Rabia, A., Mohamed, H., Ali, M., Emam, M., Faisal, R., Mohamed, S., Atta, A. (2024). 'Chebyshev spectral method for the Bratu problem', test, 1(1), pp. 23-34. doi: 10.21608/aash.2024.368286
Elhassan, A., Rabia, A., Mohamed, H., Ali, M., Emam, M., Faisal, R., Mohamed, S., Atta, A. Chebyshev spectral method for the Bratu problem. test, 2024; 1(1): 23-34. doi: 10.21608/aash.2024.368286

Chebyshev spectral method for the Bratu problem

البحوث التطبيقية في العلوم والانسانيات
Volume 1, Issue 1, July 2024, Pages 23-34    PDF (1.11 M)
Document Type: المقالة الأصلية
DOI: 10.21608/aash.2024.368286
Authors
Ahmed Abo Elhassan; Ahmed Rabia; Hamdy Mohamed; Mohamed Ali; Mohamed Emam; Rashad Faisal; Saif Elden Mohamed; Ahmed Gamal Atta
Assistant professor, Department of Mathematics Ain Shams University, Faculty of Education
Abstract
A novel and effective collocation method for solving the nonlinear Bratu differential equation is
presented in this work. The application of our spectral collocation method enables us to get a
system of nonlinear equations that solved using Newton’s iterative approach to get the
approximate solution. Furthermore, Also, numerical comparisons between the presented
procedure with different numerical methods are held. The numerical outcomes confirm that the
proposed procedure is precise, computationally efficient, and easy to implement.
Keywords
Chebyshev polynomials; Collocation method; Bratu differential equation
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