The main purpose of this paper is to solve an INVERSE random differential equation problem using evolutionary algorithms. Particle Swarm Algorithm and Genetic Algorithm are two algorithms that are used in this paper. In this paper, we solve the INVERSE problem by solving the INVERSE random differential equation using Crank-Nicholson's method. Then, using the particle swarm optimization algorithm and the genetic algorithm, we solve them. The algorithms presented in this article have advantages over other old methods that have been presented so far. Implementing these algorithms is simpler, have less run time and produce better approximation. The numerical results obtained in this paper also show that the solutions obtained for the examples presented in the numerical results section are highly accurate and have less error. All of the algorithms in this paper to obtain the desired numeric results, have been implemented on the Pentium (R) Dual core E5700 processor at 3. 00 GHz.

In this study a modified numerical scheme using meshless procedure is proposed to solve the INVERSE HEAT CONDUCTION boundary value PROBLEMS. Homotopy perturbation method (HPM) is adopted for trial functions of the collocation method used. The resultant functions are used as basis functions and an ill-conditioned system of equations is obtained by a simple collocation. To regularize the resultant ill-conditioned system of linear equations, the Tikhonov regularization technique and the L-curve were applied. Note, the approach is readily extendable to solve inhomogenous PROBLEMS. The results indicate that the approach used provides a relatively accurate scheme.

In the present work, the dual reciprocity boundary element method along with sequential function specification method is used for solution of INVERSE HEAT CONDUCTION PROBLEMS involving time and space varying HEAT flux estimation. A new version of the sequential specification method based on using polynomial fit is presented, which shows reduction in sensitivity of the solution to thermocouple locations. The results demonstrate that the method is accurate enough in cases which the amplitude of the errors is up to 2% of the maximum measured temperature. This study illustrate that, the optimum number of future time steps depends on error amplitude.

In the present paper a new scheme is presented which combines the Sequential Function Specification and the Dual Reciprocity Boundary Element Methods. In this scheme the unknown boundary condition is estimated sequentially by using two transformation matrices. The matrices defined in the direct HEAT CONDUCTION calculations by the Dual Reciprocity Boundary Element Method are used as a basis for the definition of the transformation matrices, and the mathematical derivations for the INVERSE estimation are in accordance with the Sequential Function Specification of Beck. In order to compare the speed and the accuracy of the method with the existing Sequential Function Specification Method, the exact analytical solution of a simulated test case in utilized. Results indicate an impressive improvement in the efficiency as well as the accuracy of this scheme as compared with the conventional ones. The results are accurate and stable foe error amplitudes up to one percent of measured temperatures.

A method for the analysis of INVERSE nonlinear HEAT CONDUCTION having point or line distributed HEAT sources is presented. The contribution due to the loading vector coming from either point or line HEAT sources integrals are evaluated analytically and in an exact manner. The INVERSE solution may be categorized into finding either the solution of the problem in the form of the intensity of the loading at a specific location or finding the location or orientation of the generators assuming the intensity is known. The first category is an ill-posed type problem, whereas the solution to the second category type PROBLEMS may be found by an optimization procedure. To regularize the solution to the first category type, least squares method is employed in conjunction with an addition of regularization term. To find the solution to the second category a new algorithm to be called "A Good Neighboring" is devised which make use of derivatives of order zero. For the PROBLEMS with thermal conductivity temperature dependent a nonlinear behaviour is expected which would be dealt with Kirchhoff's transformation. The efficiency and accuracy of the methods are explored through several examples.    

In this paper, an INVERSE HEAT CONDUCTION problem in one-dimensional infinite domain will be considered. By employing INVERSE HEAT fundamental solution, and an over specified condition, the temperature and its HEAT flux will be identified.

This paper deals the determination of a stable solution for an Ill-posed INVERSE HEAT CONDUCTION problem (IHCP). By using the Chebyshev polynomials base function an approximate stable solution to the IHCP will be determined in finite or infinite domain.    

In this paper, the temperature of a moving surface is determined with a moving, finite element based INVERSE method. In order to overcome the ill-condition of moving INVERSE PROBLEMS, three different conventional regularization methods are used: Levenberg, Marquardt and Modified Levenberg. The moving mesh is generated employing the transfinite mapping technique. The proposed algorithms are used in the estimation of surface temperature on a moving boundary in the burning process of a homogenous solid fuel. The measurements obtained inside the solid media are used to circumvent PROBLEMS associated with the sensor and the receding surface. As the surface recedes, the sensors are swept over by the thermal penetration depth. The produced oscillations occurring at certain intervals in the solution are a phenomenon associated with this process. It is shown that regularization delays convergence and, therefore, the use of normal analysis is sufficient. The method can be used successfully for a wide range of thermal diffusivity coefficients.