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Author(s): 

Nouri Mostafa

Issue Info: 
  • Year: 

    2020
  • Volume: 

    8
  • Issue: 

    2
  • Pages: 

    268-281
Measures: 
  • Citations: 

    0
  • Views: 

    153
  • Downloads: 

    84
Abstract: 

In this paper, a direct method for solving Volterra-Fredholm INTEGRAL equations with time delay by using orthogonal functions and their stochastic operational matrix of integration is proposed. Stochastic INTEGRAL equations can be reduced to a sparse system which can be directly solved. Numerical examples show that the proposed scheme has a suitable degree of accuracy.

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Author(s): 

Amiri Sadegh | Behrouzi Yasin

Issue Info: 
  • Year: 

    2024
  • Volume: 

    4
  • Issue: 

    1
  • Pages: 

    175-193
Measures: 
  • Citations: 

    0
  • Views: 

    18
  • Downloads: 

    0
Abstract: 

The main purpose of this paper is to propose a high order numerical method based on the finite difference methods for solving nonlinear Itˆo stochastic Volterra INTEGRAL equations (SVIEs) of the second kind. To develop the method, a fourth-order implicit finite difference method and the explicit Milstein method are implemented for the discretization of non-stochastic and stochastic INTEGRAL parts, respectively. To solve the original SVIEs, the proposed method has the deterministic fourth-order and strong stochastic first-order accuracy. The convergence analysis of the proposed method is proved. The finite difference method under consideration requires solving a 2×2 system of equations at each step for one-dimensional SVIE. Therefore, the proposed method is very simple to implement and does not require a lot of computational cost. Some numerical examples are prepared to indicate the verity and efficiency of the new method. Moreover, the comparative numerical results show that this method is more accurate than those existing methods given in the literature.

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Writer: 

TAHERI Z. | JAVADI S.

Issue Info: 
  • Year: 

    2016
  • Volume: 

    47
Measures: 
  • Views: 

    175
  • Downloads: 

    63
Abstract: 

THE PURPOSE OF THIS PAPER IS TO PROPOSE THE SPECTRAL COLLOCATION METHOD TO SOLVE LINEAR AND NONLINEAR STOCHASTIC ITÔ-VOLTERRA INTEGRAL EQUATIONS (SVIES). THE PROPOSED APPROACH IS DIFFERENT FROM EXISTING NUMERICAL TECHNIQUES AS WE CONSIDER THE LEGENDRE GAUSS TYPE QUADRATURE FOR ESTIMATING ITÔ INTEGRALS. THE MAIN CHARACTERISTIC OF THE PRESENTED METHOD IS THAT IT REDUCES SVIES INTO A SYSTEM OF ALGEBRAIC EQUATIONS. FINALLY, NUMERICAL EXAMPLES SHOW THE EFFICIENCY OF THE PROPOSED METHOD.

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Author(s): 

MIRZAEE F. | HOSEINI S.F.

Journal: 

Scientia Iranica

Issue Info: 
  • Year: 

    2015
  • Volume: 

    22
  • Issue: 

    6 (TRANSACTIONS D: COMPUTER SCIENCE AND ENGINEERING AND ELECTRICAL ENGINEERING)
  • Pages: 

    2472-2481
Measures: 
  • Citations: 

    0
  • Views: 

    469
  • Downloads: 

    296
Abstract: 

This article proposes an efficient method based on the Fibonacci functions for solving nonlinear stochastic ITO-Volterra INTEGRAL equations. For this purpose, we obtain stochastic operational matrix of Fibonacci functions. We use the proposed basis function in combination with stochastic operational matrix. This problem is then reduced into a system of nonlinear equations which can be solved by Newton's method. Also, the existence, uniqueness, and convergence of the proposed method are discussed. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is applied to some practical problems.

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Issue Info: 
  • Year: 

    2018
  • Volume: 

    4
  • Issue: 

    1
  • Pages: 

    91-104
Measures: 
  • Citations: 

    0
  • Views: 

    1161
  • Downloads: 

    351
Abstract: 

Introduction Many problems which appear in different sciences such as physics, engineering, biology, applied mathematics and different branches can be modeled by using deterministic INTEGRAL equations. Weakly singular INTEGRAL equation is one of the principle type of INTEGRAL equations which was introduced by Abel for the first time. These problems are often dependent on a noise source which are neglected due to poor computational tools. ...

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Issue Info: 
  • Year: 

    2023
  • Volume: 

    9
  • Issue: 

    1
  • Pages: 

    222-245
Measures: 
  • Citations: 

    0
  • Views: 

    22
  • Downloads: 

    0
Abstract: 

In this paper, modified hat functions and improved hat functions are proposed to solve stochastic ITO ̂-Volterra INTEGRAL equations with multi stochastic terms. A linear system of equations are achieved by replacing the vector and matrix coefficients and operational matrices in the equation which is easy to solve with mathematical softwares. Also, under some conditions the error of these methods are o(h^3) and o(h^4 ) . The accuracy and reliability of these two methods are studied by solving and comparing the answers with block pulse functions and hat functions.

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Issue Info: 
  • Year: 

    2014
  • Volume: 

    6
  • Issue: 

    1
  • Pages: 

    41-48
Measures: 
  • Citations: 

    0
  • Views: 

    781
  • Downloads: 

    223
Abstract: 

In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra INTEGRAL equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which needs specified boundary conditions. For determining boundary conditions, we use the integration technique. This technique gives an approximate simple and closed form solution for the SVIE. Expectation of the approximating process is computed. Some numerical examples are used to illustrate the accuracy of the method.

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Issue Info: 
  • Year: 

    2024
  • Volume: 

    5
  • Issue: 

    1
  • Pages: 

    33-52
Measures: 
  • Citations: 

    0
  • Views: 

    1
  • Downloads: 

    0
Abstract: 

The main objective of this article is to solve stochastic delay differential equations via Haar wavelets‎. ‎We present fundamental concepts of stochastic process‎, ‎Haar‎, ‎block pulse functions‎, ‎and their operational matrix relevant to time-delayed Haar‎. ‎Analytic solutions of two examples are solved for the first time to approximate two kinds of single time-delayed stochastic differential equations with additive and multiplicative noise‎. ‎This orthogonal basis function not only simplifies the problem but also speeds up the computations and lessens the computational complexity of the stochastic delay differential equations to a lower triangular system of linear algebraic equations‎. ‎The equation can be solved via forward substitution‎, ‎such as lower-upper decomposition method‎. ‎Finally‎, ‎we examine the order of convergence and error analysis of two visual samples to validate the efficiency and effectiveness of the suggested procedure.

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Issue Info: 
  • Year: 

    2016
  • Volume: 

    4
Measures: 
  • Views: 

    231
  • Downloads: 

    154
Abstract: 

OPTIONS ARE NANCIAL INSTRUMENTS DESIGNED TO PROTECT INVESTORS FROM THE STOCK MARKET RANDOMNESS. IN 1973 BLACK, SC-HOLES AND MERTON PROPOSED A VERY POPULAR OPTION PRICING METHOD USING STOCHASTIC DI ERENTIAL EQUATIONS WITHIN THE ITO INTERPRETATION. HEREIN, WE HAVE REVIEWED BLACK-SCHOLES THEORY USING ITO CALCULUS, WHICH IS STANDARD TO MATHEMATICAL NANCE. MOREOVER, THE BLACK-SCHOLES EQUATION OBTAINED USING STRATONOVICH CALCULUS IS THE SAME AS THE ONE OBTAINED BY MEANS OF THE ITO CALCULUS. IN FACT, THIS IS THE RESULT WE EXPECTED IN ADVANCE BECAUSE ITO AND STRATONOVICH CONVENTIONS ARE JUST DI ERENT RULES OF CALCULUS. THE OPTION PRIC-ING METHOD OBTAINS THE SO-CALLED BLACK-SCHOLES EQUATION WHICH IS A PARTIAL DI ERENTIAL EQUATION OF THE SAME KIND AS THE DI USION EQUA-TION. IN FACT, IT WAS THIS SIMILARITY THAT LED BLACK AND SCHOLES TO OBTAIN THEIR OPTION PRICE FORMULA AS THE SOLUTION OF THE DI USION EQUATION WITH THE INITIAL AND BOUNDARY CONDITIONS GIVEN BY THE OPTION CONTRACT TERMS.

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Issue Info: 
  • Year: 

    2006
  • Volume: 

    5
  • Issue: 

    14
  • Pages: 

    24-32
Measures: 
  • Citations: 

    0
  • Views: 

    6114
  • Downloads: 

    0
Abstract: 

Hypomelanosis of ITO (HI) is a heterogeneous and complex nearocutaneous disorder affecting the skin, brain, eye, skeleton, and other organs. The skin findings are distinctive and, in fact, are.the only constant feature of HI; hypopigmented whorls, streaks, and patches tend to follow Blaschko's lines. Blaschko's lines form a V-shaped pattern over the back, an S-shaped pattern over the anterior trunk, and linear streaks over the extremities.HI was first described by ITO as incontinentia pigmenti achromians, but it is now commonly known as HI to avoid confusion with incontinentia pigmenti. HI affects male and female subjects equally and is usually a sporadic disorder with minimal recurrence risk.Our patient was a 17-year-old boy who came to our clinic with tonic – clonic seizures since he was 5. He had aura before seizures as epigastric pain and facial numbness. Past medical history and family history of patient was negative. There was short of stature and macrocephaly in his physical exam. There were also V-shaped hypopigmented lesions over the back and linear over the extremities.A systolic murmur of grade I-II was heard in aortic area and chest wall of patient had a pattern of pectus excavatum. Other physical exams were normal. In neuroimaging studies, in brain MRI, there were multiple periventricular white matter lesions that were very similar to MRI findings of multiple sclerosis. As a result of our findings, clinicians should consider HI as a differential diagnosis of diseases with periventricular white matter lesions especially multiple sclerosis.

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