scholarly journals Convergence of Numerical Solution of Generalized Theodorsen’s Nonlinear Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Mohamed M. S. Nasser
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Conformal Mapping ◽  
Uniform Convergence ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Integral Equation ◽  
Numerical Results ◽  
Simply Connected

We consider a nonlinear integral equation which can be interpreted as a generalization of Theodorsen’s nonlinear integral equation. This equation arises in computing the conformal mapping between simply connected regions. We present a numerical method for solving the integral equation and prove the uniform convergence of the numerical solution to the exact solution. Numerical results are given for illustration.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

scholarly journals Numerical solution of an integral equation arising in the problem of cruciform crack using Daubechies scale function

2019 ◽  
Vol 14 (1) ◽  
pp. 21-27
Author(s):  
Jyotirmoy Mouley ◽  
M. M. Panja ◽  
B. N. Mandal
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Solution ◽  
Present Method ◽  
Numerical Results ◽  
Scale Function ◽  
Forcing Term ◽  
Classical Integral

Abstract This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for a specific forcing term are compared to those obtained by various methods available in the literature, and the present method appears to be quite accurate.

scholarly journals A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang
Keyword(s):  
Exact Solution ◽  
Numerical Methods ◽  
Error Estimate ◽  
Numerical Solution ◽  
Numerical Method ◽  
Difference Equations ◽  
Initial Value Problems ◽  
Convergence Speed ◽  
Initial Value ◽  
Delta Derivatives

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.

STABILITY ANALYSIS OF A COLLOCATION METHOD FOR SOLVING THE RETARDED POTENTIAL INTEGRAL EQUATION

2005 ◽  
Vol 13 (02) ◽  
pp. 287-299 ◽  
Author(s):  
P. J. HARRIS ◽  
H. WANG ◽  
R. CHAKRABARTI ◽  
D. HENWOOD
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Stability Analysis ◽  
Boundary Element Method ◽  
Numerical Solution ◽  
Boundary Element ◽  
Collocation Method ◽  
Stability Problem ◽  
Numerical Scheme ◽  
Type Boundary

This paper deals with the numerical solution of the retarded potential integral equation using a collocation type boundary element method. This method is widely used in practice but often suffers from stability problems. The purpose of the paper is to carry out a stability analysis of the numerical scheme and examine how any instability arises. This paper will then propose a method for overcoming this stability problem. A comparison with an exact solution demonstrates that the approach proposed here is effective for the case of a sphere.

scholarly journals A New Numerical Algorithm for Two-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Lihua Guo ◽  
Boying Wu ◽  
Dazhi Zhang
Keyword(s):  
Exact Solution ◽  
Error Analysis ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Numerical Algorithm ◽  
Numerical Stability ◽  
Boundary Value ◽  
Numerical Results ◽  
Point Boundary ◽  
Stability And Error Analysis

We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that then-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.

scholarly journals Solving Volterra Integrodifferential Equations via Diagonally Implicit Multistep Block Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Nur Auni Baharum ◽  
Zanariah Abdul Majid ◽  
Norazak Senu
Keyword(s):  
Stability Analysis ◽  
Numerical Solution ◽  
Numerical Method ◽  
Numerical Computation ◽  
Numerical Solutions ◽  
Numerical Results ◽  
Integrodifferential Equations ◽  
Block Method ◽  
The Stability ◽  
Predictor Corrector

The performance of the numerical computation based on the diagonally implicit multistep block method for solving Volterra integrodifferential equations (VIDE) of the second kind has been analyzed. The numerical solutions of VIDE will be computed at two points concurrently using the proposed numerical method and executed in the predictor-corrector (PECE) mode. The strategy to obtain the numerical solution of an integral part is discussed and the stability analysis of the diagonally implicit multistep block method was investigated. Numerical results showed the competence of diagonally implicit multistep block method when solving Volterra integrodifferential equations compared to the existing methods.

Unsteady Loads on Supercavitating Hydrofoils of Finite Span

1966 ◽  
Vol 10 (02) ◽  
pp. 107-118
Author(s):  
Sheila Evans Widnall
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Integral Equations ◽  
Digital Computer ◽  
High Speed ◽  
Three Dimensional ◽  
Numerical Results ◽  
Oscillatory Motion ◽  
Surface Theory ◽  
Finite Span

Linearized three-dimensional lifting-surface theory is derived for a supercavitating hydrofoil with finite span in steady or oscillatory motion through an infinite fluid. The resulting coupled-integral equations are solved on a high-speed digital computer using a numerical method of assumed modes similar to that used for fully wetted surfaces. Numerical results for lift and moment for both steady and oscillating foils are compared with other theories and experiments. Results of these calculations indicate that this numerical solution gives an efficient and accurate prediction of loads on a supercavitating foil.

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