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An integral transformation, a coordinate transformation for immobilization of the moving boundary, and orthogonal collocation are used to reduce a nonlinear initial-boundary value problem in time and space to a set of ordinary differential equations in time with given initial conditions.
Our aim is to apply a mathematical transformation to reduce a nonlinear equation to linear equation diffusivity, for a naturally fractured system.
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Ravi Kanth and Bhattacharya [5] used a quasi-linearization technique to reduce a class of nonlinear SBVP arising in physiology to a sequence of linear problems; the resulting set of differential equations is modified at the singular point, then spline collocation is utilized to obtain the numerical solution.
To reduce "chattering" a nonlinear observer with estimation of the mechanical torque and rotor fluxes is designed.
In the so-called Spitzer Härm regime, equations of plasma physics reduce to a nonlinear parabolic equation for the electronic temperature.
By using Galerkin's approach, the nonlinear governing partial differential equation is reduced to a nonlinear ordinary differential equation.
Given the data and constraints, the calibration then reduces to a nonlinear constraint maximization problem, which has a unique solution.
It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation.
By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof.
Based on the Galerkin's decomposition method, the nonlinear PDE governing equation is reduced to a nonlinear ordinary differential equation (ODE).
The resulting design avoids the solution of computationally intensive dynamic optimizations since the integration of design and control problem is reduced to a nonlinear constrained optimization problem.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com