The modified Kawahara (mKawahara) equation is a cubic non-linear equation with a fifth-order derivative term. The quadratic nonlinear form of the equation is suggested by Kawahara  with its steady solutions. Such solutions may exist due to the sign of the dispersive term and these solutions can be in a oscillatory form because of the dominant fifth-ordered term. The mKawahara equation has implicit doubly periodic solutions and they can be determined by using the method of auxiliary equation[13, 14]. Some soliton and periodic solutions are derived by using a set of forecasting methods having some trigonometric and hyperbolic functions inside. The mKawahara equation has also non-constant meromorphic solutions in explicit form. The existence of traveling wave type solutions in hyperbolic or trigonometric forms are discussed by Al-Ali. Tanh and exp-function methods are also capable to derive the exact solutions to the mKawahara equation. So far, some methods belonging to different categories have been proposed for the exact solutions of both integer or fractional ordered PDEs [19, 20, 21, 22]. In ths study ,The main aim is to derive some exact solutions to the three-dimensional conformable time fractional KP and the conformable time fractional mKawahara equations. The solutions are obtained explicitly by using modifiedKudryashovmethod. The existence of the chain rule and other required properties in the defi- nition of the conformable derivative enable some wave transformations to generate the solutions.
In this paper, the modiﬁed Kudryashovmethod is proposed to solve fractional diﬀerential equations, and Jumarie’s modiﬁed Riemann-Liouville derivative is used to convert nonlinear partial fractional diﬀerential equation to nonlinear ordinary diﬀerential equations. The modiﬁed Kudryashovmethod is applied to compute an approximation to the solutions of the space-time fractional modiﬁed
The exact solutions of some conformable time fractional PDEs are pre- sented explicitly. The modifiedKudryashovmethod is applied to construct the solutions to the conformable time fractional Regularized Long Wave- Burgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker’s parabolic (CRWP) equations. Initially, the predicted so- lution in the finite series of a rational form of an exponential function is substituted to the ODE generated from the conformable time fractional PDE by using wave transformation. The coefficients used in the finite series are determined by solving the algebraic system derived from the coefficients of the powers of the predicted solution.
To obtain the best execution time for a particular benchmark, all four synchronization methods should be executed by specifying the method at runtime. A program might benefit if we vary the synchronization mode between different regions of code. To incorporate such dynamic synchronization, the synchronization method should be able to be varied at every session. This result in a speedup when compared to the best execution time obtained from executing the four methods on an individual basis. But such aggressive switching might incur some overhead. Sliding-window method overcomes this problem by maintaining a particular method for a number of sessions before changing it to another synchronization method.
Finding the edges of street-level fisheye images is even harder than satellite images due to the high variations of intensities, objects and distortion. Figure 5.3 (first and second rows) shows some sample street-level images that Otsu’s method did not work well for them. Also Figure 5.3 (third row) shows our effort to improve the results of Otsu’s method by adding an offset to the Otsu’s threshold (like what we did for the satellite images). However, this is not practical, because to get the best result we had to set the offset for each of the images of a chain individually. More importantly, in some of these images (like the 1st and 2nd column) it is impossible to separate the roads from the rest of the image even by carefully setting the offset. The reason is that the intensity histogram of these images is not separable at all into two modes (foreground and background).
of a simulation problem to an initial value problem is then described. Sections 5 and 6 respec- tively contain reviews of two well-known methods for solving initial value problems; namely, Euler’s method and the modified midpoint method. The use of Richardson’s extrapolation is discussed in each case with the aid of a simple numerical example. Linear representations of a non-linear economic model are set out in section 7, where the practicalities of applying each of the foregoing methods are assessed in some detail. In the eighth and final section a tentative agenda for future research is sketched.
The steps to compare the estimation methods for missing data begun by step one by the selection of one station to represent station with the missing value. Step two comprises a pace to remove 5% of data from selected stations. Step three used the remaining data and data from neighboring stations to estimate the missing values using M method, NR method, MNR method, and CCW method followed. Step four was the performances of each estimation method are compared using the correlation coefficient (R), the similarity index (S-index), the root mean squared error (RMSE) and mean absolute error (MAE). Finally, step two and four repeated for 10% and 15% missing values.
We present cyclic models for systems with two renewable resources. In modelling, the interactions and the reciprocal influences between these two resources are taken into ac- count. Analysis of the models is carried out in weighted Holder spaces. A method for the solution of the balance system of equations is proposed. The equilibrium state of the system is found.
5. Recognition – The recognition engine will take data from either a newly captured subject via the feature extraction module, or a previously stored signature, and perform recognition based on a database of test subjects. The modified CPN model did not require training parameters because it is not an iterative method like back- propagation architecture which took a long time for learning. Rather, a minimum error value is specified initially and the weights are estimated based on the specified error value and this is what accounts for higher convergence rate of the model since one set of weights are estimated directly.
so presented combined preconditioners, which are given by combinations of R with any upper preconditioner, and showed that the convergence rate of the combined meth- ods are better than those of the Gauss-Seidel method ap- plied with other upper preconditioners . In , Niki et al. considered the preconditioner P SR = I S R .
processing of a wide range of materials, both living and fos- sil. It involves two main chemicals, kerosene and kitchen drain cleaner fluid, both of which are cheap, easy to obtain, and easy to discard afterwards. Kerosene, used here as a sub- stitute for naphtha in the Oda and Sato method (2013), is a familiar fuel oil for room heaters or hot water supply systems in Japan, while the kitchen drain cleaning fluid can be bought at a reasonable cost at supermarkets, drug stores, or do-it- yourself or daily grocery shops in Japan. Similar nonacidic products are also available in other countries. However, if acidic products are used the calcareous microfossils includ- ing coccoliths will be dissolved, so care must be taken when choosing the kitchen drain cleaner fluid.
Next, the controlled solutions at times 0.2 ms, 1 ms and 2 ms using the MDY method are shown in Figure 6. Observe that the excitation wavefront is unable to be dampened out by the applied current, and the excitation wavefront continue to spread to the computational do- main. This phenomenon happens because the MDY me- thod failed to converge to the optimal solution during the optimization process.
Routing method accuracy and application depends on basic assumptions inherent in the method. Researchers have performed studies trying to determine which routing method is best suited to a certain routing situation. Strelkoff (1980) compared the kinematic model, diffusion model, and modified Puls method with the complete Saint Venant equations as a basis for comparison. Floodplains, simple channels, and downstream boundary conditions were considered in the study. He found that the diffusion model produced results most comparable to the Saint Venant equations. The other methods produce acceptable results under certain conditions, as described in the
This paper proposes a modified synchronization approach to make the synchronization practicable in the situation when the direct signal is unsatisfactory, and the parameters of the transmitted signal are even unknown. Both the experiment results of imaging and BiInSAR results verified the effectiveness of the proposed approach.
In this paper, the Black-Scholes equation is solved by using the Adomian’s decomposition method , modified Adomian’s decomposition method , variational iteration method , modified variational iteration method, ho- motopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed methods are proved in details. A numerical example is studied to demonstrate the accuracy of the presented methods.
An alternative method is a test-centered method whereby the pass mark is based on item or station char- acteristics, such as the modified Angoff standard setting method. In the modified Angoff methods, judges reviewed each question after defining a borderline candi- date, and decided whether the borderline examinee will respond correctly [2, 6, 13, 14]. The main advantage of such a method is that the pass/fail standard can be reliably set before the OSCE is undertaken, which would be useful in the setting of CBME [2, 15, 16]. Furthermore, a modi- fied Angoff could potentially be used to set different pass marks for junior and senior residents, eliminating the need for two end of rotation OSCEs.
I t namic problems in physics and other fields has been shown that many important dy- are usually characterized by nonlinear evolution equations which are often called governing equa- tions [3, 42, 36, 27]. To understand the physical mechanism of these problems one has to study the solutions to the associated governing equations. Searching for the exact solutions of the nonlin- ear physical models has been a major concern for both mathematicians and physicists since they can provide much physical information and more insight into the physical aspects of the problems and thus maybe lead to further applications. Re- cently, some mathematician have studied the nu- merical solution of the Degasperis-Procesi equa- tion by numerical method [28, 21, 12, 29, 32, 20].