**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**8081

# Search results for: Jacobi method

##### 8081 Preconditioned Jacobi Method for Fuzzy Linear Systems

**Authors:**
Lina Yan,
Shiheng Wang,
Ke Wang

**Abstract:**

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

**Keywords:**
preconditioning,
M-matrix,
Jacobi method,
fuzzy linear
system (FLS).

##### 8080 Jacobi-Based Methods in Solving Fuzzy Linear Systems

**Authors:**
Lazim Abdullah,
Nurhakimah Ab. Rahman

**Abstract:**

Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

**Keywords:**
Fuzzy linear systems,
Jacobi,
Jacobi Over-
Relaxation,
Refinement of Jacobi,
Refinement of Jacobi Over-
Relaxation.

##### 8079 Complexity Reduction Approach with Jacobi Iterative Method for Solving Composite Trapezoidal Algebraic Equations

**Authors:**
Mohana Sundaram Muthuvalu,
Jumat Sulaiman

**Abstract:**

In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.

**Keywords:**
Complexity reduction approach,
Composite trapezoidal
scheme,
Jacobi method,
Linear Fredholm integral equations

##### 8078 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices

**Authors:**
Zuan-De Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

**Keywords:**
Backward USSOR iterative matrix,
Jacobi iterative matrix,
convergence,
spectral radius

##### 8077 On the Algorithmic Iterative Solutions of Conjugate Gradient, Gauss-Seidel and Jacobi Methods for Solving Systems of Linear Equations

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
H. N. Ude

**Abstract:**

In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

**Keywords:**
conjugate gradient,
linear equations,
symmetric and positive definite matrix,
Gauss-Seidel,
Jacobi,
algorithm

##### 8076 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices

**Authors:**
Zhuan-de Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

**Keywords:**
Backward MPSD iterative matrix,
Jacobi iterative matrix,
eigenvalue,
p-cyclic matrix.

##### 8075 A New Approach to the Approximate Solutions of Hamilton-Jacobi Equations

**Authors:**
Joe Imae,
Kenjiro Shinagawa,
Tomoaki Kobayashi,
Guisheng Zhai

**Abstract:**

We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of ‘virtual-time’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.

**Keywords:**
Nonlinear Control,
Optimal Control,
Hamilton-Jacobi Equation,
Virtual-Time

##### 8074 A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society

**Authors:**
Weihua Ruan,
Kuan-Chou Chen

**Abstract:**

**Keywords:**
Differential games,
Hamilton-Jacobi-Bellman
equations,
infinite horizon,
political-economy models.

##### 8073 Numerical Study of Iterative Methods for the Solution of the Dirichlet-Neumann Map for Linear Elliptic PDEs on Regular Polygon Domains

**Authors:**
A. G. Sifalakis,
E. P. Papadopoulou,
Y. G. Saridakis

**Abstract:**

**Keywords:**
Elliptic PDEs,
Dirichlet to Neumann Map,
Global Relation,
Collocation,
Iterative Methods,
Jacobi,
Gauss-Seidel,
GMRES,
Bi-CGSTAB.

##### 8072 Application of Legendre Transformation to Portfolio Optimization

**Authors:**
Peter Benneth,
Tsaroh N. Theophilus,
Prince Benjamin

**Abstract:**

This research work aims at studying the application of Legendre Transformation Method (LTM) to Hamilton Jacobi Bellman (HJB) equation which is an example of optimal control problem. We discuss the steps involved in modelling the HJB equation as it relates to mathematical finance by applying the Ito’s lemma and maximum principle theorem. By applying the LTM and dual theory, the resultant HJB equation is transformed to a linear Partial Differential Equation (PDE). Also, the Optimal Investment Strategy (OIS) and the optimal value function were obtained under the exponential utility function. Furthermore, some numerical results were also presented with observations that the OIS under exponential utility is directly proportional to the appreciation rate of the risky asset and inversely proportional to the instantaneous volatility, predetermined interest rate, risk averse coefficient. Finally, it was observed that the optimal fund size is an increasing function of the risk free interest rate. This result is consistent with some existing results.

**Keywords:**
Legendre transformation method,
Optimal investment strategy,
Ito’s lemma,
Hamilton Jacobi Bellman equation,
Geometric Brownian motion,
financial market.

##### 8071 On the Solution of Fully Fuzzy Linear Systems

**Authors:**
Hsuan-Ku Liu

**Abstract:**

A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.

**Keywords:**
Fully fuzzy linear equations,
iterative method,
homotopy perturbation method,
approximate solutions.

##### 8070 Optimal Portfolio Selection in a DC Pension with Multiple Contributors and the Impact of Stochastic Additional Voluntary Contribution on the Optimal Investment Strategy

**Authors:**
Edikan E. Akpanibah,
Okwigbedi Oghen’Oro

**Abstract:**

In this paper, we studied the optimal portfolio selection in a defined contribution (DC) pension scheme with multiple contributors under constant elasticity of variance (CEV) model and the impact of stochastic additional voluntary contribution on the investment strategies. We assume that the voluntary contributions are stochastic and also consider investments in a risk free asset and a risky asset to increase the expected returns of the contributing members. We derived a stochastic differential equation which consists of the members’ monthly contributions and the invested fund and obtained an optimized problem with the help of Hamilton Jacobi Bellman equation. Furthermore, we find an explicit solution for the optimal investment strategy with stochastic voluntary contribution using power transformation and change of variables method and the corresponding optimal fund size was obtained. We discussed the impact of the voluntary contribution on the optimal investment strategy with numerical simulations and observed that the voluntary contribution reduces the optimal investment strategy of the risky asset.

**Keywords:**
DC pension fund,
Hamilton-Jacobi-Bellman,
optimal investment strategies,
power transformation method,
stochastic,
voluntary contribution.

##### 8069 An Approximation Method for Three Quark Systems in the Hyper-Spherical Approach

**Authors:**
B. Rezaei,
G. R. Boroun,
M. Abdolmaleki

**Abstract:**

The bound state energy of three quark systems is studied in the framework of a non- relativistic spin independent phenomenological model. The hyper- spherical coordinates are considered for the solution this system. According to Jacobi coordinate, we determined the bound state energy for (uud) and (ddu) quark systems, as quarks are flavorless mass, and it is restrict that choice potential at low and high range in nucleon bag for a bound state.

**Keywords:**
Adiabatic expansion,
grand angular momentum,
binding energy,
perturbation,
baryons.

##### 8068 On Algebraic Structure of Improved Gauss-Seidel Iteration

**Authors:**
O. M. Bamigbola,
A. A. Ibrahim

**Abstract:**

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

**Keywords:**
Linear system of equations,
Gauss-Seidel iteration,
algebraic structure,
convergence.

##### 8067 An Insurer’s Investment Model with Reinsurance Strategy under the Modified Constant Elasticity of Variance Process

**Authors:**
K. N. C. Njoku,
Chinwendu Best Eleje,
Christian Chukwuemeka Nwandu

**Abstract:**

One of the problems facing most insurance companies is how best the burden of paying claims to its policy holders can be managed whenever need arises. Hence there is need for the insurer to buy a reinsurance contract in order to reduce risk which will enable the insurer to share the financial burden with the reinsurer. In this paper, the insurer’s and reinsurer’s strategy is investigated under the modified constant elasticity of variance (M-CEV) process and proportional administrative charges. The insurer considered investment in one risky asset and one risk free asset where the risky asset is modeled based on the M-CEV process which is an extension of constant elasticity of variance (CEV) process. Next, a nonlinear partial differential equation in the form of Hamilton Jacobi Bellman equation is obtained by dynamic programming approach. Using power transformation technique and variable change, the explicit solutions of the optimal investment strategy and optimal reinsurance strategy are obtained. Finally, some numerical simulations of some sensitive parameters were obtained and discussed in details where we observed that the modification factor only affects the optimal investment strategy and not the reinsurance strategy for an insurer with exponential utility function.

**Keywords:**
Reinsurance strategy,
Hamilton Jacobi Bellman equation,
power transformation,
M-CEV process,
exponential utility.

##### 8066 Mean-Variance Optimization of Portfolios with Return of Premium Clauses in a DC Pension Plan with Multiple Contributors under Constant Elasticity of Variance Model

**Authors:**
Bright O. Osu,
Edikan E. Akpanibah,
Chidinma Olunkwa

**Abstract:**

In this paper, mean-variance optimization of portfolios with the return of premium clauses in a defined contribution (DC) pension plan with multiple contributors under constant elasticity of variance (CEV) model is studied. The return clauses which permit death members to claim their accumulated wealth are considered, the remaining wealth is not equally distributed by the remaining members as in literature. We assume that before investment, the surplus which includes funds of members who died after retirement adds to the total wealth. Next, we consider investments in a risk-free asset and a risky asset to meet up the expected returns of the remaining members and obtain an optimized problem with the help of extended Hamilton Jacobi Bellman equation. We obtained the optimal investment strategies for the two assets and the efficient frontier of the members by using a stochastic optimal control technique. Furthermore, we studied the effect of the various parameters of the optimal investment strategies and the effect of the risk-averse level on the efficient frontier. We observed that the optimal investment strategy is the same as in literature, secondly, we observed that the surplus decreases the proportion of the wealth invested in the risky asset.

**Keywords:**
DC pension fund,
Hamilton Jacobi Bellman equation,
optimal investment strategies,
stochastic optimal control technique,
return of premiums clauses,
mean-variance utility.

##### 8065 Effect of Supplementary Premium on the Optimal Portfolio Policy in a Defined Contribution Pension Scheme with Refund of Premium Clauses

**Authors:**
Edikan E. Akpanibah Obinichi C. Mandah Imoleayo S. Asiwaju

**Abstract:**

In this paper, we studied the effect of supplementary premium on the optimal portfolio policy in a defined contribution (DC) pension scheme with refund of premium clauses. This refund clause allows death members’ next of kin to withdraw their relative’s accumulated wealth during the accumulation period. The supplementary premium is to help sustain the scheme and is assumed to be stochastic. We considered cases when the remaining wealth is equally distributed and when it is not equally distributed among the remaining members. Next, we considered investments in cash and equity to help increase the remaining accumulated funds to meet up with the retirement needs of the remaining members and composed the problem as a continuous time mean-variance stochastic optimal control problem using the actuarial symbol and established an optimization problem from the extended Hamilton Jacobi Bellman equations. The optimal portfolio policy, the corresponding optimal fund size for the two assets and also the efficient frontier of the pension members for the two cases was obtained. Furthermore, the numerical simulations of the optimal portfolio policies with time were presented and the effect of the supplementary premium on the optimal portfolio policy was discussed and observed that the supplementary premium decreases the optimal portfolio policy of the risky asset (equity). Secondly we observed a disparity between the optimal policies for the two cases.

**Keywords:**
Defined contribution pension scheme,
extended Hamilton Jacobi Bellman equations,
optimal portfolio policies,
refund of premium clauses,
supplementary premium.

##### 8064 Several Spectrally Non-Arbitrary Ray Patterns of Order 4

**Authors:**
Ling Zhang,
Feng Liu

**Abstract:**

A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern *A *of order *n *is called spectrally arbitrary if the complex matrices in the ray pattern class of *A* give rise to all possible *n*th degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern*.* We call that a spectrally arbitrary ray pattern *A *of order *n *is minimally spectrally arbitrary if any nonzero entry of *A* is replaced, then *A *is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

**Keywords:**
Spectrally arbitrary,
Nilpotent matrix,
Ray patterns,
sign patterns.

##### 8063 Using Spectral Vectors and M-Tree for Graph Clustering and Searching in Graph Databases of Protein Structures

**Authors:**
Do Phuc,
Nguyen Thi Kim Phung

**Abstract:**

**Keywords:**
Eigenvalues,
m-tree,
graph database,
protein
structure,
spectra graph theory.

##### 8062 Non-Local Behavior of a Mixed-Mode Crack in a Functionally Graded Piezoelectric Medium

**Authors:**
Nidhal Jamia,
Sami El-Borgi

**Abstract:**

In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

**Keywords:**
Functionally graded piezoelectric material,
mixed-mode crack,
non-local theory,
Schmidt method.

##### 8061 Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model

**Authors:**
Amadi Ugwulo Chinyere,
Lewis D. Gbarayorks,
Emem N. H. Inamete

**Abstract:**

In this paper, the mandatory contribution, additional voluntary contribution (AVC) and administrative charges are merged together to determine the optimal investment strategy (OIS) for a pension plan member (PPM) in a defined contribution (DC) pension scheme under the modified constant elasticity of variance (M-CEV) model. We assume that the voluntary contribution is a stochastic process and a portfolio consisting of one risk free asset and one risky asset modeled by the M-CEV model is considered. Also, a stochastic differential equation consisting of PPM’s monthly contributions, voluntary contributions and administrative charges is obtained. More so, an optimization problem in the form of Hamilton Jacobi Bellman equation which is a nonlinear partial differential equation is obtained. Using power transformation and change of variables method, an explicit solution of the OIS and the value function are obtained under constant absolute risk averse (CARA). Furthermore, numerical simulations on the impact of some sensitive parameters on OIS were discussed extensively. Finally, our result generalizes some existing result in the literature.

**Keywords:**
DC pension fund,
modified constant elasticity of variance,
optimal investment strategies,
voluntary contribution,
administrative charges.

##### 8060 Explicit Solution of an Investment Plan for a DC Pension Scheme with Voluntary Contributions and Return Clause under Logarithm Utility

**Authors:**
Promise A. Azor,
Avievie Igodo,
Esabai M. Ase

**Abstract:**

The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.

**Keywords:**
Legendre transform,
logarithm utility,
optimal distribution plan,
return clause of premium,
charge on balance,
Weibull mortality function.

##### 8059 Weighted Harmonic Arnoldi Method for Large Interior Eigenproblems

**Authors:**
Zhengsheng Wang,
Jing Qi,
Chuntao Liu,
Yuanjun Li

**Abstract:**

The harmonic Arnoldi method can be used to find interior eigenpairs of large matrices. However, it has been shown that this method may converge erratically and even may fail to do so. In this paper, we present a new method for computing interior eigenpairs of large nonsymmetric matrices, which is called weighted harmonic Arnoldi method. The implementation of the method has been tested by numerical examples, the results show that the method converges fast and works with high accuracy.

**Keywords:**
Harmonic Arnoldi method,
weighted harmonic Arnoldi method,
eigenpair,
interior eigenproblem,
non symmetric matrix.

##### 8058 Dissipation of Higher Mode using Numerical Integration Algorithm in Dynamic Analysis

**Authors:**
Jin Sup Kim,
Woo Young Jung,
Minho Kwon

**Abstract:**

**Keywords:**
Dynamic,
α-Method,
P-Method,
PC α-Method,
Newmark method.

##### 8057 The RK1GL2X3 Method for Initial Value Problems in Ordinary Differential Equations

**Authors:**
J.S.C. Prentice

**Abstract:**

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

**Keywords:**
RK1GL2X3,
RK1GL2,
RKrGLm,
Runge-Kutta,
Gauss-Legendre,
initial value problem,
local error,
global error.

##### 8056 Seat Assignment Problem Optimization

**Authors:**
Mohammed Salem Alzahrani

**Abstract:**

**Keywords:**
Assignment Problem,
Hungarian Method,
Least Cost
Method,
Northwest Corner Method,
Seat Assignment Method
(SAM),
A Real Word Assignment Problem.

##### 8055 A New Method to Solve a Non Linear Differential System

**Authors:**
Seifedine Kadry

**Abstract:**

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

**Keywords:**
Continuation Method,
Newton Method,
Finite Difference Method,
Numerical Analysis and Non-Linear partial Differential Equation.

##### 8054 An Efficient Method for Solving Multipoint Equation Boundary Value Problems

**Authors:**
Ampon Dhamacharoen,
Kanittha Chompuvised

**Abstract:**

**Keywords:**
Boundary value problem; Multipoint equation
boundary value problems,
Shooting Method,
Newton-Broyden
method.

##### 8053 The Differential Transform Method for Advection-Diffusion Problems

**Authors:**
M. F. Patricio,
P. M. Rosa

**Abstract:**

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

**Keywords:**
Method of Lines,
Differential Transform Method.

##### 8052 HPL-TE Method for Determination of Coatings Relative Total Emissivity Sensitivity Analysis of the Influences of Method Parameters

**Abstract:**

High power laser – total emissivity method (HPL-TE method) for determination of coatings relative total emissivity dependent on the temperature is introduced. Method principle, experimental and evaluation parts of the method are described. Computer model of HPL-TE method is employed to perform the sensitivity analysis of the effect of method parameters on the sample surface temperature in the positions where the surface temperature and radiation heat flux are measured.

**Keywords:**
High temperature laser testing,
measurement ofthermal properties,
emissivity,
coatings.