Newton’s Method Applied to Problems in Nonlinear Mechanics

1965 ◽  
Vol 32 (2) ◽  
pp. 383-388 ◽  
Author(s):  
G. A. Thurston
Keyword(s):  
Boundary Value Problems ◽  
Newton’S Method ◽  
Newton's Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Practical Method ◽  
Algebraic Equations ◽  
Nonlinear Mechanics ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

Many problems in mechanics are formulated as nonlinear boundary-value problems. A practical method of solving such problems is to extend Newton’s method for calculating roots of algebraic equations. Three problems are treated in this paper to illustrate the use of this method and compare it with other methods.

The generalized fractional order of the Chebyshev functions on nonlinear boundary value problems in the semi-infinite domain

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
Kourosh Parand ◽  
Mehdi Delkhosh
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Fractional Order ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Numerical Results ◽  
Algebraic Equations ◽  
Nonlinear Boundary Value Problems ◽  
Infinite Domain ◽  
Nonlinear Boundary Value

AbstractA new collocation method, namely the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) collocation method, is given for solving some nonlinear boundary value problems in the semi-infinite domain, such as equations of the unsteady isothermal flow of a gas, the third grade fluid, the Blasius, and the field equation determining the vortex profile. The method reduces the solution of the problem to the solution of a nonlinear system of algebraic equations. To illustrate the reliability of the method, the numerical results of the present method are compared with several numerical results.

Sign in / Sign up

Export Citation Format

Share Document