TELLURIC FIELD AND APPARENT RESISTIVITY OVER AN INCLINED NORMAL FAULT

1965 ◽  
Vol 2 (4) ◽  
pp. 351-360 ◽  
Author(s):  
P. S. Naidu
Keyword(s):  
Boundary Value Problem ◽  
Apparent Resistivity ◽  
Analytic Solution ◽  
Boundary Value ◽  
Normal Fault ◽  
Numerical Results ◽  
Conformai Mapping ◽  
Basement Fault

The telluric field and apparent resistivity anomalies caused by an inclined normal fault are calculated along a profile perpendicular to the strike of the fault. The method of conformai mapping is used to obtain an analytic solution of the boundary value problem. Numerical results are presented in the form of a series of graphs. It is concluded that the angle of inclination for a basement fault can be determined quantitatively for a large throw or qualitatively for a moderate throw.The effect of anisotropic strata on the anomaly curves is discussed.

scholarly journals An approximate analytic solution of a particular boundary value problem

2001 ◽  
Vol 27 (8) ◽  
pp. 513-520
Author(s):  
Ugur Tanriver ◽  
Aravinda Kar
Keyword(s):  
Boundary Value Problem ◽  
Heat Conduction Equation ◽  
Analytic Solution ◽  
Boundary Value ◽  
Three Dimensional ◽  
Welding Process ◽  
Approximate Analytic Solution ◽  
Analytic Expression ◽  
Steady State Heat ◽  
Laser Welding Process

This note is concerned with the three-dimensional quasi-steady-state heat conduction equation subject to certain boundary conditions in the wholex′y′-plane and finite inz′-direction. This type of boundary value problem arises in laser welding process. The solution to this problem can be represented by an integral using Fourier analysis. This integral is approximated to obtain a simple analytic expression for the temperature distribution.

On the analytic solution of the helical equilibrium equation in the MHD approximation

1975 ◽  
Vol 14 (2) ◽  
pp. 305-314 ◽  
Author(s):  
M. L. Woolley
Keyword(s):  
Boundary Value Problem ◽  
Hypergeometric Functions ◽  
Analytic Solution ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Hydrodynamic Pressure ◽  
Additional Information ◽  
Countably Infinite ◽  
Infinite Set ◽  
Well Posed

The second-order elliptic partial differential equation, which describes a class of static ideally conducting magnetohydrodynamic equilibria with helical symmetry, is solved analytically. When the equilibrium is contained within an infinitely long conducting cylinder, the appropriate Dirichiet boundary-value problem may be solved in general in terms of hypergeometric functions. For a countably infinite set of particular cases, these functions are polynomials in the radial co-ordinate; and a solution may be obtained in a closed form. Necessary conditions are given for the existence of the equilibrium, which is described by the simplest of these functions. It is found that the Dirichlet boundary-value problem is not well-posed for these equiilbria; and additional information (equivalent to locating a stationary value of the hydrodynamic pressure) must be provided, in order that the solution be unique.

scholarly journals THE ANALYTIC SOLUTION OF INITIAL BOUNDARY VALUE PROBLEM INCLUDING TIME FRACTIONAL DIFFUSION EQUATION

2020 ◽  
Vol 35 (1) ◽  
pp. 243
Author(s):  
Süleyman Çetinkaya ◽  
Ali Demir ◽  
Hülya Kodal Sevindir
Keyword(s):  
Boundary Value Problem ◽  
Analytic Solution ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
One Dimension ◽  
Sturm Liouville ◽  
Fractional Differential ◽  
Initial Boundary Value

The motivation of this study is to determine the analytic solution of initial boundary value problem including time fractional differential equation with Neumann boundary conditions in one dimension. By making use of seperation of variables, the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem.

A General Approximate Solution for Stretching Problems in Viscous Fluid

2015 ◽  
Vol 70 (9) ◽  
pp. 781-786
Author(s):  
Saleem Asghar ◽  
Mudassar Jalil ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Boundary Value Problem ◽  
Analytic Solution ◽  
Boundary Value ◽  
Skin Friction Coefficient ◽  
Order System ◽  
First Order ◽  
Exponential Stretching ◽  
Special Cases

AbstractIn this study, we propose a boundary value problem that contains two arbitrary parameters in the differential equation and show that the results of a number of existing stretching problems (linear, power law, and exponential stretching) are the special cases of the proposed boundary value problem. A two-term analytic asymptotic solution of this problem is developed by introducing a small parameter in the differential equation. Interest lies in the finding of rare exact analytical solutions for the zeroth and first order systems. Surprisingly, only a two-term closed form of analytical solution shows an excellent match with the existing literature. The solution for second-order system is found numerically to improve the accuracy of the approximate solution. The generalised analytic solution is tested over a number of stretching problems for the velocity field and skin friction coefficient showing an excellent match. In conclusion, various stretching problems discussed in literature are special cases of this study.

Thermoelasticity of an Anisotropic Half Space

1974 ◽  
Vol 41 (4) ◽  
pp. 935-940 ◽  
Author(s):  
J. Padovan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Half Space ◽  
Boundary Value ◽  
Integral Transforms ◽  
Numerical Results ◽  
Heat Sinks ◽  
Material Anisotropy ◽  
Body Forces

The thermoelasticity of an anisotropic Hookean half space is studied herein. A solution based on successive integral transforms is developed. The solution can handle arbitrary thermal and mechanical boundary conditions together with distributed body forces and heat sinks or sources. To illustrate the substantial effects of material anisotropy, a specific boundary-value problem is solved. Numerical results based on the solution are presented. These illustrate the significant effects of both thermal and mechanical material anisotropy.

scholarly journals Numerical Solution of Singularly Perturbed Two Parameter Problems using Exponential Splines

2021 ◽  
Vol 26 (2) ◽  
pp. 160-172
Author(s):  
P. Padmaja ◽  
P. Aparna ◽  
Rama Subba Reddy Gorla ◽  
N. Pothanna
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Shishkin Mesh ◽  
Numerical Results ◽  
Singularly Perturbed ◽  
Perturbation Parameters ◽  
Two Parameter

Abstract In this paper, we have studied a method based on exponential splines for numerical solution of singularly perturbed two parameter boundary value problems. The boundary value problem is solved on a Shishkin mesh by using exponential splines. Numerical results are tabulated for different values of the perturbation parameters. From the numerical results, it is found that the method approximates the exact solution very well.

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