The Series Solution Method

2016 ◽  
pp. 375-393
Author(s):  
Svetlin G. Georgiev
Keyword(s):  
Series Solution ◽  
Solution Method

Solving a system of Volterra-Fredholm integral equation of the second kind via series solution method

2014 ◽  
Vol 8 ◽  
pp. 2181-2194
Author(s):  
Nejmaddin A. Sulaiman ◽  
Shahraddin bin Sallah ◽  
Talhat I. Hassan
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Series Solution ◽  
Solution Method

Axisymmetric Free-Vibration Problems by Boundary Element Method

1988 ◽  
Vol 55 (2) ◽  
pp. 437-442 ◽  
Author(s):  
Hui-Ching Wang ◽  
Prasanta K. Banerjee
Keyword(s):  
Finite Element Method ◽  
Free Vibration ◽  
Boundary Element ◽  
Vibration Analysis ◽  
Series Solution ◽  
Solution Method ◽  
Free Vibration Analysis ◽  
Element Formulation ◽  
Vibration Problems ◽  
Element Method

A new boundary-element formulation using particular integrals is developed for the free-vibration analysis of axisymmetric solids. The numerical results for a number of axisymmetric free-vibration problems are given and some of the results are compared with those obtained from Finite Element Method, Series Solution Method, or experimental method. Generally, agreement among all of these results is satisfactory.

scholarly journals A Series-Solution Method for Cometary Orbits

1972 ◽  
Vol 45 ◽  
pp. 43-51
Author(s):  
P. E. Nacozy
Keyword(s):  
Series Solution ◽  
Solution Method ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Reference Solution ◽  
Successive Interval ◽  
First Order ◽  
Order Solution ◽  
The Mean ◽  
The Masses

A series-solution method for highly-eccentric perturbed orbits using a modified form of Hansen's method of partial anomalies is presented. Series in Chebyshev polynomials in the eccentric anomaly of a comet and the mean anomaly at an epoch of a planet provide a theory valid to first order with respect to the masses. The first-order solution becomes a reference solution about which higher-order perturbations are obtained by the method of successive approximations. The first-order solutions are valid approximations for long durations of time, whereas the higher orders are valid only over the interval of time that is selected for the Chebyshev expansions. The method is somewhat similar to Encke's method of special perturbations except that for each successive interval of time perturbations about a first-order solution are calculated instead of perturbations about a conic solution.

scholarly journals Power Series Solution for Solving Nonlinear Burgers-Type Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
E. López-Sandoval ◽  
A. Mello ◽  
J. J. Godina-Nava ◽  
A. R. Samana
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Series Solution ◽  
Solution Method ◽  
Nonlinear Partial Differential Equations ◽  
Time Dependent ◽  
Power Series Solution ◽  
Partial Linear ◽  
Linear Differential ◽  
Burgers Type Equations

Power series solution method has been traditionally used to solve ordinary and partial linear differential equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-type differential equations in order to demonstrate its scope and applicability.

scholarly journals Tank Drainage for an Electrically Conducting Newtonian Fluid with the use of the Bessel Function

2020 ◽  
Vol 10 (2) ◽  
pp. 5377-5381
Author(s):  
M. A. Khaskheli ◽  
K. N. Memon ◽  
A. H. Sheikh ◽  
A. M. Siddiqui ◽  
S. F. Shah
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Unsteady Flow ◽  
Flow Rate ◽  
Average Velocity ◽  
Series Solution ◽  
Solution Method ◽  
Electrically Conducting ◽  
Velocity Flow ◽  
Time Required

In this study, an unsteady flow for drainage through a circular tank of an isothermal and incompressible Newtonian magnetohydrodynamic (MHD) fluid has been investigated. The series solution method is employed, and an analytical solution is obtained. Expressions for the velocity field, average velocity, flow rate, fluid depth at different times in the tank and time required for the wide-ranging drainage of the fluid (time of efflux) have been obtained. The Newtonian solution is attained by assuming σΒ02=0. The effects of various developing parameters on velocity field υz and depth of fluid H(t) are presented graphically. The time needed to drain the entire fluid and its depth are related and such relations are obtained in closed form. The effect of electromagnetic forces is analyzed. The fluid in the tank will drain gradually and it will take supplementary time for complete drainage.

Sign in / Sign up

Export Citation Format

Share Document