- 期刊
FAST-CONVERGENCE ITERATIVE ALGORITHMS FOR SOLVING A NONLINEAR BEAM EQUATION WITH AN INTEGRAL TERM SUBJECTED TO DIFFERENT BOUNDARY CONDITIONS
摘要
In this paper, a nonlinear beam equation containing an integral term of the deformation energy, which is unknown before the solution is found, is investigated under different boundary conditions. First, we set the unknown integral term as a scalar variable and then develop a weak-form integral equation to solve the integral. By using the sinusoidal functions as test functions and bases of the numerical solution, we obtain a fast-convergence iterative scheme. Due to the orthogonality of the sinusoidal functions, the expansion coefficients of the numerical solution are in the closed form. The proposed iterative algorithms converge quickly and provide highly accurate numerical solutions of the nonlinear beam equation containing the integral term, as confirmed using five numerical examples.
延伸閱讀
- 林罡亦（2009）。Application of Nonlinear Autoregressive with Exogenous Input Model to Estimate the Linear Modal Parameters of Nonlinear Systems〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2009.00087
- Santos, M. L., Ferreira, J., & Raposo, C. A. (2005). EXISTENCE AND UNIFORM DECAY FOR A NONLINEAR BEAM EQUATION WITH NONLINEARITY OF KIRCHHOFF TYPE IN DOMAINS WITH MOVING BOUNDARY. Abstract and Applied Analysis, 2005(), 901-919. https://doi.org/10.1155/AAA.2005.901
- Caballero, J., Darwish, M. A., Sadarangani, K., & Shammakh, W. M. (2014). Existence Results for a Coupled System of Nonlinear Fractional Hybrid Differential Equations with Homogeneous Boundary Conditions. Abstract and Applied Analysis, 2014(), 99-108-1111. https://doi.org/10.1155/2014/672167
- Nasertayoob, P., Vaezpour, S. M., & Baleanu, D. (2014). Solvability for a Coupled System of Fractional Integrodifferential Equations with m-Point Boundary Conditions on the Half-Line. Abstract and Applied Analysis, 2014(), 682-688-376. https://doi.org/10.1155/2014/297314
- Ceng, L. C., Latif, A., & Mazrooei, A. E. A. (2014). Iterative Algorithms for Systems of Generalized Equilibrium Problems with the Constraints of Variational Inclusion and Fixed Point Problems. Abstract and Applied Analysis, 2014(), 489-512-850. https://doi.org/10.1155/2014/540381