scholarly journals Analytic Solution to Shell Boundary - Value Problems

2015 ◽  
Author(s):  
Yuri Vinogradov
Keyword(s):  
Boundary Value Problems ◽  
Analytic Solution ◽  
Boundary Value ◽  
Shell Boundary

Contemporary Methods for the Numerical-Analytic Solution of Boundary-Value Problems in Noncanonical Domains

2020 ◽  
Vol 247 (1) ◽  
pp. 88-107
Author(s):  
P. Shakeri Mobarakeh ◽  
V. T. Grinchenko ◽  
V. V. Popov ◽  
B. Soltannia ◽  
G. M. Zrazhevsky
Keyword(s):  
Boundary Value Problems ◽  
Analytic Solution ◽  
Boundary Value

scholarly journals Galerkin Method for Nonlinear Higher-Order Boundary Value Problems Based on Chebyshev Polynomials

2021 ◽  
Vol 2128 (1) ◽  
pp. 012035
Author(s):  
W. Abbas ◽  
Mohamed Fathy ◽  
M. Mostafa ◽  
A. M. A Hesham
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Chebyshev Polynomials ◽  
Nonlinear Boundary ◽  
Analytic Solution ◽  
Boundary Value ◽  
Higher Order ◽  
Nonlinear Boundary Value Problems ◽  
Algebraic Set ◽  
The Galerkin Method

Abstract In the current paper, we develop an algorithm to approximate the analytic solution for the nonlinear boundary value problems in higher-order based on the Galerkin method. Chebyshev polynomials are introduced as bases of the solution. Meanwhile, some theorems are deducted to simplify the nonlinear algebraic set resulted from applying the Galerkin method, while Newton’s method is used to solve the resulting nonlinear system. Numerous examples are presented to prove the usefulness and effectiveness of this algorithm in comparison with some other methods.

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