Article

1998 ◽  
Vol 76 (7) ◽  
pp. 539-557
Author(s):  
M Burgess ◽  
M Carrington ◽  
G Kunstatter
Keyword(s):  
Initial Value Problem ◽  
Wave Motion ◽  
Generalized Functions ◽  
Incompressible Fluids ◽  
Horizontal Direction ◽  
Wave Number ◽  
Initial Value ◽  
Two Fluids ◽  
Wave Maker

The initial value problem of wave motion is considered for two immiscible layersof incompressible fluids in the presence of a porous wave maker immersed vertically in thetwo uids, which are periodic in the horizontal direction along the wave maker as well as intime. The resulting motion is investigated using the method of generalized functions, and anasymptotic analysis for large values of time and distance is given for the depression of thefree surface and the surface of separation between the two fluids. The generated fluid patternis discussed for different values of the wave number of the oscillations of the wave makervelocity in the horizontal direction. PACS No.: 47.35

scholarly journals Transient development of gravity waves for two layered fluids

1992 ◽  
Vol 15 (2) ◽  
pp. 333-338 ◽  
Author(s):  
A. H. Essawy ◽  
M. S. Faltas
Keyword(s):  
Free Surface ◽  
Asymptotic Analysis ◽  
Gravity Waves ◽  
Initial Value Problem ◽  
Large Time ◽  
Generalized Functions ◽  
Incompressible Fluids ◽  
Initial Value ◽  
Wave Maker

The transient gravity waves generated by a harmonically oscillating wave maker immersed in two incompressible fluids, the upper fluid having a free surface, is considered. The resulting linearized initial value problem is solved using the method of generalized functions, and asymptotic analysis for large time and distance are given for the elevation.

Forced gravity waves in two-layered fluids with the upper fluid having a free surface

2003 ◽  
Vol 81 (4) ◽  
pp. 675-689 ◽  
Author(s):  
H H Sherief ◽  
M S Faltas ◽  
E I Saad
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Harmonic Wave ◽  
Density Ratio ◽  
Finite Depth ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Two Fluids ◽  
Lower Fluid ◽  
Wave Maker

The steady-gravity wave motion is considered for two immiscible layers of incompressible and nonviscous fluids in the presence of a porous wave maker immersed vertically in the two fluids, the upper fluid having a free surface and the lower fluid is of infinite depth. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the wave maker. Also the scattering of a harmonic wave incident normally to the wave maker is considered and the reflection and transmission coefficients are obtained. The case when the lower fluid is of finite depth is also considered. The results are plotted for different values of porosity and different values of the density ratio. PACS Nos.: 47.35.+i, 47.55.Hd, 47.55.Mh

scholarly journals Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

scholarly journals A Neural Network Technique for the Derivation of Runge-Kutta Pairs Adjusted for Scalar Autonomous Problems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1842
Author(s):  
Vladislav N. Kovalnogov ◽  
Ruslan V. Fedorov ◽  
Yuri A. Khakhalev ◽  
Theodore E. Simos ◽  
Charalampos Tsitouras
Keyword(s):  
Neural Network ◽  
Differential Evolution ◽  
Initial Value Problem ◽  
Fitness Function ◽  
Initial Value ◽  
Runge Kutta

We consider the scalar autonomous initial value problem as solved by an explicit Runge-Kutta pair of orders 6 and 5. We focus on an efficient family of such pairs, which were studied extensively in previous decades. This family comes with 5 coefficients that one is able to select arbitrarily. We set, as a fitness function, a certain measure, which is evaluated after running the pair in a couple of relevant problems. Thus, we may adjust the coefficients of the pair, minimizing this fitness function using the differential evolution technique. We conclude with a method (i.e. a Runge-Kutta pair) which outperforms other pairs of the same two orders in a variety of scalar autonomous problems.

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