Analytical-Numeric Formulas for the Probability Density Function of Multivariate Stable and Geo-Stable Distributions

Fallahgoul, Hasan; Hashemiparast, S. M.; Fabozzi, Frank J.; Klebanov, Lev B.

doi:10.1080/15598608.2013.780989

Cited by 4 publications

(4 citation statements)

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“…The reason for this is to express equation (1) in the canonical form in order to employ ADM. Our approach invokes the reflexive equivalence property of equality, where we have advantageously added the solution to both sides of equation (1). Following the ADM, the unknown solution w (x) is assumed to be the decomposition series of the form:…”

Section: Fredholm Integral Equations Of the First Kindmentioning

confidence: 99%

“…By substitution of the recursive scheme equation (4) into equation (3), we conclude that the ADM for equation (1) can be converted to an equivalent problem, which we state as follows. Theorem 1.…”

Section: Fredholm Integral Equations Of the First Kindmentioning

confidence: 99%

“…Convergence analysis of ADM In this section, we will discuss the result concerning the convergence analysis of the ADM for equation (1). Theorem 2.…”

Section: Fredholm Integral Equations Of the First Kindmentioning

confidence: 99%

“…The key idea of this technique is based on transforming equation(1) into the regularization integral equation:Kðx; tÞw 1 ðtÞdt ¼ f ðxÞ;ð26Þwhere 1 . 0.…”

mentioning

confidence: 99%

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A convenient technique for solving integral equations of the first kind by the Adomian decomposition method

Bougoffa

Al‐Haqbani

Rach³

2012

Kybernetes

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If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -In this paper, Fredholm integral equations of the first kind, the Schlomilch integral equation, and a class of related integral equations of the first kind with constant limits of integration are transformed in such a manner that the Adomian decomposition method (ADM) can be applied. Some examples with closed-form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient. The purpose of this paper is to develop a new iterative procedure where the integral equations of the first kind are recast into a canonical form suitable for the ADM. Hence it examines how this new procedure provides the exact solution. Design/methodology/approach -The new technique, as presented in this paper in extending the applicability of the ADM, has been shown to be very efficient for solving Fredholm integral equations of the first kind, the Schlomilch integral equation and a related class of nonlinear integral equations with constant limits of integration. Findings -By using the new proposed technique, the ADM can be easily used to solve the integral equations of the first kind, the Schlomilch integral equation, and a class of related integral equations of the first kind with constant limits of integration. Originality/value -The paper shows that this new technique is easy to implement and produces accurate results.

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Section: Fredholm Integral Equations Of the First Kindmentioning

confidence: 99%

Section: Fredholm Integral Equations Of the First Kindmentioning

confidence: 99%

“…Convergence analysis of ADM In this section, we will discuss the result concerning the convergence analysis of the ADM for equation (1). Theorem 2.…”

Section: Fredholm Integral Equations Of the First Kindmentioning

confidence: 99%

“…The key idea of this technique is based on transforming equation(1) into the regularization integral equation:Kðx; tÞw 1 ðtÞdt ¼ f ðxÞ;ð26Þwhere 1 . 0.…”

mentioning

confidence: 99%

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