Nonlinear solver — Scalar Newton

Nonlinear solverPASS · <0.01%

Nonlinear iteration, tangent, path-following, and state-management verification. Checks: Newton update convergence order and stopping criteria.

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Problem statement

Geometry: Solve x^3-2=0 from x0=1.5 with exact derivative.
Material: Constitutive or analytical definition: x_(n+1)=x_n-(x_n^3-2)/(3x_n^2).
Boundary conditions: Required solver capability: newton_driver. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Root=1.25992104989; x1=1.2962962963; asymptotic e_(n+1)/e_n^2 -> 0.793700525984.

Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:

scalar equation f="x^3 - 2" x0=1.5
solve newton maxiter=10 tol=1e-14
extract root convergence_ratio

Reference value	root=1.25992104989, x1=1.2962962963, ratio=0.793701
Our result	root=1.25992104989, x1=1.2962962963, ratio=0.793659
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	Scalar cubic benchmark x^3 - 2 = 0, exact quadratic error convergence

Updated: 2026-10-27 · version not recorded