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## Archive of Issues

Russia; Vietnam Moscow; Tuyen Quang
Year
2019
Volume
29
Issue
1
Pages
61-72
 Section Mathematics Title Pseudospectral method for second-order autonomous nonlinear differential equations Author(-s) Nhat L.A.ab Affiliations Peoples' Friendship University of Russia (RUDN University)a, Tan Trao Universityb Abstract Autonomous nonlinear differential equations constituted a system of ordinary differential equations, which often applied in different areas of mechanics, quantum physics, chemical engineering science, physical science, and applied mathematics. It is assumed that the second-order autonomous nonlinear differential equations have the types ${u}''({x}) - {u}'({x}) = {f}[{u}({x})]$ and ${u}''({x}) + {f}[{u}({x})]{u}'({x}) + {u}({x}) = 0$ on the range $[-1, 1]$ with the boundary values ${u}[-1]$ and ${u}[1]$ provided. We use the pseudospectral method based on the Chebyshev differentiation matrix with Chebyshev-Gauss-Lobatto points to solve these problems. Moreover, we build two new iterative procedures to find the approximate solutions. 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