scholarly journals One-Dimensional Heat Conduction in a Semi-infinite Solid With the Surface Temperature a Harmonic Function of Time: A Simple Approximate Solution for the Transient Behavior

1990 ◽  
Vol 112 (4) ◽  
pp. 1076-1079 ◽  
Author(s):  
P. Burow ◽  
B. Weigand
Keyword(s):  
Approximate Solution ◽  
Heat Conduction ◽  
Harmonic Function ◽  
Surface Temperature ◽  
Transient Behavior ◽  
One Dimensional ◽  
Simple Approximate Solution

scholarly journals Enthalpy method for one dimensional heat conduction

2018 ◽  
Vol 7 (2.14) ◽  
pp. 9
Author(s):  
Farah Suraya Md Nasrudin ◽  
Shafaruniza Mahadi
Keyword(s):  
Approximate Solution ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Finite Difference Method ◽  
Moving Boundary ◽  
Nonlinear Differential Equations ◽  
Melting Process ◽  
Technical Grade ◽  
One Dimensional ◽  
Enthalpy Method

In this paper, the Enthalpy Method is employed to compute an approximate solution of the system of nonlinear differential equations focusing on the simulation of moving boundary for one dimensional heat conduction. This paper is only considered in the problem of a technical grade paraffin’s melting process. In order to seek the solution in term of temperature distribution, Finite Difference Method will be used. The results obtained are compared between solving with enthalpy and without enthalpy. The enthalpy method is more versatile, convenient, adaptable and easily programmable.  

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

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