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Equilibrium Problems in Systems with a Finite Number
Eigenvalue Problems for Systems with a Finite Number
Propagation Problems in Systems with a Finite Number
5 other sections not shown
algorithm applied approximate solution beam boundary conditions buckling characteristics coefficients column computation constant continuous system convergence corresponding decimal places deflection derivatives determining diagonal differential equations dimensionless discretization error domain eigenvalue problem eigenvector elements equilibrium problem essential boundary essential boundary conditions Euler's method evaluated exact solution example Exercise extraneous solution extrapolation extremum problem finite finite-difference approximation formulation function Galerkin Galerkin method given governing equations Green's function illustrate initial conditions initial trial integral interval iteration load Math mode nondimensional obtained operations orthogonal parameters positive definite potential energy procedure propagation problem Rayleigh's quotient recurrence formula residual Ritz method round-off error satisfy Schwarz quotients self-adjoint sequence Show shown in Fig Simpson's rule solving square matrix stationary step symmetric Table tion transverse trial family trial solution truncation error values vanish variables Verify vibrating zero