Ship Centerplane Source Distribution

A procedure for calculating the irrotational flow about a double ship model, by solving a Fredholm integral equation of the first kind for a centerplane source distribution, is described. The special problems of determining the curve in the centerplane bounding the source distribution and of smoothing sharply peaking inte-grands, to improve the accuracy of discretization of the integral equation, are treated. Application to ellipsoids, for which the results of the calculations can be compared with an exact solution, and to a ship form with parabolic lines, for which experimental data are available for comparison, indicate that satisfactory accuracy can be obtained by the method. A justification for using a centerplane distribution is that, as is shown, a line integral which appears in the higher-order solution for the flow about a ship form at nonzero Froude numbers can be avoided with such a distribution.

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Approximate Solution of Nonlinear Integral Equations of the Second Kind by Using Homotopy Perturbation Method

Dhaka University Journal of Science ◽

10.3329/dujs.v65i2.54527 ◽

2017 ◽

Vol 65 (2) ◽

pp. 151-155

Author(s):

MM Hasan ◽

MA Matin

Keyword(s):

Integral Equation ◽

Exact Solution ◽

Approximate Solution ◽

Perturbation Method ◽

Fredholm Integral Equation ◽

Homotopy Perturbation Method ◽

Nonlinear Integral Equations ◽

Numerical Examples ◽

Homotopy Perturbation ◽

Nonlinear Fredholm Integral Equation

In this paper, we apply Homotopy perturbation method (HPM) for obtaining approximate solution of nonlinear Fredholm integral equation of the second kind. Finally, some numerical examples are provided, and the obtained numerical approximations are compared with the corresponding exact solution. Dhaka Univ. J. Sci. 65(2): 151-155, 2017 (July)

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An Approximate Solutions of two Dimension Linear Mixed Volterra- Fredholm Integral Equation of the Second Kind via Iterative Kernel Method

Journal of Raparin University ◽

10.26750/vol(6).no(2).paper7 ◽

2019 ◽

Vol 6 (2) ◽

pp. 101-110

Author(s):

Talaat Ismael Hasan

Keyword(s):

Integral Equation ◽

Exact Solution ◽

Fredholm Integral Equation ◽

Kernel Method ◽

Approximate Solutions ◽

Least Square ◽

Computer Application ◽

Numerical Examples ◽

Running Time ◽

Two Dimension

Abstract: In this work, we reformulate and apply iterative kernel method (IKM) for solving two dimension mixed Volterra-Fredholm integral equation of the second kind (MVFIE-2). The suitable algorithm for IKM is suggested and the programming for of the algorithm of the technique is written by Matlab programs. The computer application for the algorithm is tested on a number numerical examples. The results which are obtained by this technique compared with exact solution and some new theorems are proved; for decision the results computing the least square error (LSE) of the IKM and running time (RT) for the program.

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Some Probability Characteristics Functions of the Solution of a Stochastic Non-Linear Fredholm Integral Equation of the Second Kind

Baghdad Science Journal ◽

10.21123/bsj.8.2.394-399 ◽

2011 ◽

Vol 8 (2) ◽

pp. 394-399

Author(s):

Baghdad Science Journal

Keyword(s):

Integral Equation ◽

Exact Solution ◽

Spectral Density ◽

Probability Density ◽

Fredholm Integral Equation ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Adomian Decomposition ◽

Non Linear

In this research, some probability characteristics functions (probability density, characteristic, correlation and spectral density) are derived depending upon the smallest variance of the exact solution of supposing stochastic non-linear Fredholm integral equation of the second kind found by Adomian decomposition method (A.D.M)

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Representation of the exact solution and a stability analysis on the Fredholm integral equation of the first kind in reproducing kernel space

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.05.049 ◽

2006 ◽

Vol 182 (2) ◽

pp. 1608-1614 ◽

Cited By ~ 6

Author(s):

Hong Du ◽

Minggen Cui

Keyword(s):

Integral Equation ◽

Exact Solution ◽

Stability Analysis ◽

Fredholm Integral Equation ◽

Reproducing Kernel ◽

Kernel Space ◽

Reproducing Kernel Space

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The Numerical Analysis of an Antenna near a Dielectric Object Using the Higher-Order Characteristic Basis Function Method Combined with a Volume Integral Equation

IEICE Transactions on Communications ◽

10.1587/transcom.e97.b.2066 ◽

2014 ◽

Vol E97.B (10) ◽

pp. 2066-2073 ◽

Cited By ~ 5

Author(s):

Keisuke KONNO ◽

Qiang CHEN

Keyword(s):

Integral Equation ◽

Numerical Analysis ◽

Basis Function ◽

Function Method ◽

Higher Order ◽

Volume Integral ◽

Volume Integral Equation

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On Improved Approximate Solution of the Fredholm Integral Equation

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2006-0014 ◽

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.

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