On modified Black–Scholes equation

Ahmed, E.; Abdusalam, H. A.

doi:10.1016/j.chaos.2004.02.018

Cited by 21 publications

(9 citation statements)

References 8 publications

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“…Recent studies such as dynamics [10], chemical [6], economical and biological processes [11] have shown that delay differential equation plays an important role in explaining many different phenomena. One of the well know delay differential equations which is an important feature in reaction-diffusion and convection-diffusion systems [1,7,8] are time delayed Burgers equation. Moreover, the generalized time-delayed Burgers equation is presented in [8,16].…”

Section: Introductionmentioning

confidence: 99%

Hypercomplex mathematics and HPM for the time-delayed Burgers equation with convergence analysis

Rostamy

Karimi

2011

Numer Algor

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We investigate the analytical and numerical solutions of the timedelayed Burgers equation, by applying the idea of commutative hypercomplex mathematics and the homotopy perturbation method. Moreover, we discuss at great length the convergence conditions of the homotopy perturbation Method (HPM) by using the Banach fixed point theory , which could provide a good iteration algorithm. Finally, we also give some numerical illustrations to the obtained results.

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Section: Introductionmentioning

confidence: 99%

Hypercomplex mathematics and HPM for the time-delayed Burgers equation with convergence analysis

Rostamy

Karimi

2011

Numer Algor

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“…One of the well-known partial differential equations (PDEs) which governs a wide variety of them is Burgers equation, which provides the simplest nonlinear model of turbulence [5]. The existence of relaxation time or delay time is an important feature in reaction diffusion and convection diffusion systems [9,1,3].…”

Section: Introductionmentioning

confidence: 99%

On the exact and numerical solution of the time-delayed Burgers equation

Fahmy¹,

Raslan²,

Abdusalam³

2008

International Journal of Computer Mathematics

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“…The parabolic-hyperbolic equation (2.1), known in engineering and in physics as a damped wave or telegrapher's equation, is often encountered in various fields besides physics (e.g., in statistics [5], [11]; finance [2]; transmission of signals over telegraph wires (hence the terminology); and many more [9], [31]). It has also been thoroughly investigated from a mathematical viewpoint [1], [7], [17], [29].…”

Section: B Elastic Sheet Approachmentioning

confidence: 99%

“…An improved mode1 that accounts for inertia results in the telegrapher's equation (see, for example, [2] and the references therein, or [14]). In the latter case, the speed of propagation is (Fig.…”

Section: E Why Ted?mentioning

confidence: 99%

Denoising-Enhancing Images on Elastic Manifolds

Ratner

Zeevi

2011

IEEE Trans. on Image Process.

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Abstract-The conflicting demands for simultaneous low-pass and high-pass processing, required in image denoising and enhancement, still present an outstanding challenge, although a great deal of progress has been made by means of adaptive diffusion-type algorithms. To further advance such processing methods and algorithms, we introduce a family of second-order (in time) partial differential equations. These equations describe the motion of a thin elastic sheet in a damping environment. They are also derived by a variational approach in the context of image processing. The new operator enables better edge preservation in denoising applications by offering an adaptive lowpass filter, which preserves high-frequency components in the pass-band better than the adaptive diffusion filter, while offering slower error propagation across edges. We explore the action of this powerful operator in the context of image processing and exploit for this purpose the wealth of knowledge accumulated in physics and mathematics about the action and behavior of this operator. The resulting methods are further generalized for color and/or texture image processing, by embedding images in multidimensional manifolds. A specific application of the proposed new approach to superresolution is outlined.

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On modified Black–Scholes equation

Cited by 21 publications

References 8 publications

Hypercomplex mathematics and HPM for the time-delayed Burgers equation with convergence analysis

Hypercomplex mathematics and HPM for the time-delayed Burgers equation with convergence analysis

On the exact and numerical solution of the time-delayed Burgers equation

Denoising-Enhancing Images on Elastic Manifolds

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