Solving nonlinear heat transfer problems using variation of parameters

Approximation of Solutions of Nonlinear Heat Transfer Problems

We develop a generalized approximation method (GAM) to obtain solution of a steady state one-dimensional nonlinear convective-radiative-conduction equation. The GAM generates a bounded monotone sequence of solutions of linear problems. The sequence of approximants converges monotonically and rapidly to a solution of the original problem. We present some numerical simulation to illustrate and co...

Solving Nonlinear Estimation Problems Using Splines

W e describe the use of splines for solv-i n g n o n l i n e a r model estimation problems, in which nonlinear functions with unknown shapes and values are involved, by converting the nonlinear estimation problems into linear ones at a higher-dimensional space. This contrasts with the typical use of the splines [1]–[3] for function interpolation where the functional values at some input points ...

Solving nonlinear eigenvalue problems

NONLINEAR CONTROL OF HEAT TRANSFER DYNAMIC USING HOMOTOPY PERTURBATION METHOD (HPM)

Nonlinear problems are more challenging and almost complex to be solved. A recently developed Homotopy Perturbation Method (HPM) is introduced. This method is used to represent the system as a less complicated (almost linear) model. To verify the effectiveness, HPM based model is compared with the nonlinear dynamic in both open and closed loop PI controlled. The error indices are approximation ...

SFE method using Hermite polynomials: An approach for solving nonlinear mechanical problems with uncertain parameters

We propose a stochastic finite element method for nonlinear mechanical systems whose uncertain parameters can be modeled as random variables. This method is based on a Gaussian standardization of the problem and on an Hilbertian approximation of the nonlinear mechanical function using Hermite polynomials. The coefficients of the approximation are obtained using a cubic B-spline interpolation of...