Analytical solution for fuzzy heat equation based on generalized Hukuhara differentiability

2015 ◽  
pp. 251-255
Author(s):  
T Allahviranloo ◽  
Z Gouyandeh ◽  
A Armand
Keyword(s):  
Analytical Solution ◽  
Heat Equation ◽  
Generalized Hukuhara Differentiability

scholarly journals Transforming Arithmetic Asian Option PDE to the Parabolic Equation with Constant Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Zieneb Ali Elshegmani ◽  
Rokiah Rozita Ahmad ◽  
Saiful Hafiza Jaaman ◽  
Roza Hazli Zakaria
Keyword(s):  
Parabolic Equation ◽  
Analytical Solution ◽  
Heat Equation ◽  
Numerical Solution ◽  
Closed Form ◽  
Asian Option ◽  
Asian Options ◽  
New Approach ◽  
Constant Coefficients ◽  
Closed Form Analytical Solution

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

Analytical solution to heat equation with magnetic resonance experimental verification for nanoshell enhanced thermal therapy

2008 ◽  
Vol 40 (9) ◽  
pp. 660-665 ◽  
Author(s):  
Andrew Elliott ◽  
Jon Schwartz ◽  
James Wang ◽  
Anil Shetty ◽  
John Hazle ◽  
...  
Keyword(s):  
Magnetic Resonance ◽  
Analytical Solution ◽  
Heat Equation ◽  
Experimental Verification ◽  
Thermal Therapy

scholarly journals Propagação do calor em uma barra homogênea com condições de fronteira e dependendo de um parâmetro real

1981 ◽  
Vol 3 (3) ◽  
pp. 01
Author(s):  
Lilian M. Kieling Reis ◽  
Vanilde Bisognin
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Initial Condition

In this work the permanent temperature, in one homogeneous bar with boundary conditions that depends of a real parameters, was determined. The problem to be resolved was find the analytical solution of the heat equation ut =α2 uxx with the initial condition u (x, 0) = 0, ≤ x ≤ L and the contours conditions u (0, t) = 0 and u (L, t) = sen t, t> 0.

scholarly journals Thermal Load and Heat Transfer in Dental Titanium Implants: an Exact Analytical Solution to the ‘Heat Equation’

2021 ◽  
Author(s):  
Ziyad S. Haidar
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Heat Equation ◽  
Exposure Time ◽  
Thermal Load ◽  
Exact Analytical Solution ◽  
Titanium Implants ◽  
Surrounding Tissue ◽  
Temperature Changes

Introduction: Heat is a kinetic process whereby energy flows from between two systems; hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and -drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury; this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants upon hot-liquid intake. Materials and Methods: We investigate the impact of the material, the location point along implant length, and the exposure time of the thermal load on temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of knowledge, this is the first introduction of the intrinsic time, a “proper” time that characterizes the geometry of the dental implant, where we show, mathematically and graphically, how the interplay between “proper” time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability and success rates, whether for immediate or delayed loading strategies.

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