Generalized integral transform

GENERALIZED INTEGRAL TRANSFORMATIONS, A.H. Zemanian. Graduate-level study of recent generalizations of the Laplace, Mellin, Hankel, K. Weierstrass, convolution and other simple transformations. Bibliography. 320pp. 5H x 8H. 65375-7 Pa. 7.95... 

The present section reviews the concepts behind the Generalized Integral Transform Technique (GITT) [35-40] as an example of a hybrid method in convective heat transfer applications. The GITT adds to tiie available simulation tools, either as a companion in co-validation tasks, or as an alternative approach for analytically oriented users. We first illustrate the application of this method in the full transformation of a typical convection-diffusion problem, until an ordinary differential system is obtained for the transformed potentials. Then, the more recently introduced strategy of... 

This work discusses hybrid numerical-analytical solutions and mixed symbolic-numerical algorithms for solving transient fully developed flow and transient forced convection in micro-channels, making use of the Generalized Integral Transform Technique (GITT) and the Mathematica system. 

A.H.Zemanian, Generalized Integral Transformations. Dover Pub. Inc. New York (1987). 

The general integral transform of a function fit) is defined as follows ... 

Zemanian, A. H., Generalized Integral Transformations, Mineola, NY Dover Publications, 1987. 

All the theoretical work was performed by making use of mixed symbolic-numerical computation via the Mathematica 7.0 platform [22], and a hybrid numerical-analytical methodology with automatic error control, the Generalized Integral Transform Technique - GITT [23-26], in handling the governing partial differential equations. 

Equations (6) are now solved by the Generalized Integral Transform Technique, GITT, starting with the choice of an appropriate filtering solution that eliminates the non-homogeneous terms in the equation and boundary conditions ... 

Liu, C., J.E. Szecsody, J.M, Zachara, and W.P, Ball, Use of the generalized integral transform method for solving equations of solute transport in porous media. Advances in Water Resourses, 2000, 23 pp, 483 92... 

We shall return to the subject of Hilbert space when we will deal with the generalized integral transform. For the present, let us return to the solution Euclidean space, if we know the projection on the coordinate K as y,K ), the function y can be reconstructed in terms of a linear combination of all, countably infinite, coordinates hence. 

Before we demonstrate the method of generalized integral transforms, we convert the dimensional mass balance equations into dimensionless form. This... 

This set of equations (Eqs. 11.184) can be solved readily by the Laplace transform method, as was done in Problem 10.17. Here we are going to apply the method of generalized integral transforms to solve this set of equations. 

Defining this matrix operator is the second key step in the methodology of the generalized integral transform method. The operator L applied onto an element ft will give another element also lying in the same space (Fig. 11.10). 

Thus, we have cast the variables in the original equations into a format of a functional space. To apply the generalized integral transform, we need to endow our function space with an inner product that is, an operation between two... 

As we have observed with the Sturm-Liouville integral transform and we will observe later for this generalized integral transform, there will arise an infinite set of eigenvalues and an infinite set of corresponding eigenfunctions. We then rewrite Eqs. 11.191 to 11.193 as follows to represent the nth values... 

This example summarizes all the necessary steps for the generalized integral transform. To recap the technique, we list below the specific steps to apply this technique. 

Apply the generalized integral transform method to solve the following problem... 

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