Abstract: A change of variables that stabilizes numerical computations for periodic solutions of autonomous systems is derived. Computation of the period is decoupled from the rest of the problem for ...

Abstract: A modification of Newton’s method is suggested that provides a practical means of continuing solutions of nonlinear differential equations through limit points or bifurcation points. The method ...

Abstract: A numerical solution is obtained for the nonlinear equations for clamped, shallow spherical shells under external pressure. Results are presented in the postbuckling range which have not been ...

Abstract: A numerical method is outlined for computing roots of determinants of lambda matrices. Convergence of the method is quadratic as long as the derivative of the determinant does not vanish at ...

Abstract: 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. ...

Abstract: A modification of Newton’s method is applied to the solution of the nonlinear differential equations for clamped, shallow spherical caps under uniform pressure. The linear form of Newton’s method ...

Abstract: Application of Newton’s method to nonlinear vibration problems can lead to a sequence of nonhomogeneous ordinary differential equations with periodic coefficients. The form of the complementary ...