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Anyone, please help me to check these sentences...Thanks a lot..

The ABC, DEF and GHI method were derived and implemented in Chapter 2, 3 and 4 respectively for solving DVPs directly. These three developed methods have their own respective codes. It would be interesting to combine all these three methods in a single code in order to make a variable step variable order method.

Another beneficial field/area/way of further research is implement/run these proposed method under parallel computing environment since the computation of this current approach is more expensive as the order of the method increase.

It may be of interest to do a particular trivial modification in the proposed method in order to make it numerically stable since the stability decreases as the order of the method increase.

Mister Micawber · Accepted Answer

The ABC, DEF and GHI methods for solving DVPs directly were derived and implemented in Chapter 2, 3 and 4 respectively. These three methods have their own respective codes. It would be interesting to combine all three in a single code in order to create a variable-step, variable-order method.

Another promising area for further research would be to implement these methods under parallel computing environments, since the computation used in this current approach becomes more expensive as the order of the method increases.

It may also be of interest to investigate specific minor modifications in the method in order to increase its numerical stablility, since stability decreases as the order of the method increases.

Myvi · Answer

This is the complement for my text. Thanks a lot..

This thesis focuses on solving A, however solving B problem is another interesting issue to be taken into account. By developing a sophisticated method that comprises the differentiation (for A) and integration (for B) approach which can solve both classes of problems is extremely interesting even though it may be very difficult and tough to do. Then it will definitely give a good impact in this research area.

Furthermore, it will be worthwhile to think further research about extending this method for solving C equations, D equations and E equations.

One potentially step is design a software that contain this method for solving higher-order DVPs directly since from literature/knowledge there was no existing mathematical software which solve the higher-order DVPs directly.

Mister Micawber · Answer

This thesis focuses on solving A. However, solving B is another interesting issue to be considered. Developing a sophisticated method that combines the differentiation (A) and the integration (B) approach in order to solve both classes of problems would be extremely interesting, even though it may be very difficult to accomplish, and it would significantly impact this research area.

It would also be worthwhile to consider further research on expanding this method to solve C equations, D equations and E equations. One potential step would be to design software that utilizes this method to solve higher-order DVPs directly, since no such software yet exists, at least in the literature.

Myvi · Answer

Tau and Hu (2005) employed ABC method based on ZZ formula for solving higher-order BDEs directly. The authors designed the explicit method for computing the solutions at seven points simultaneously with utilizing constant step size. An implicit DEF method based on YY formula for solving first-order DVPs has been developed by Richard et al. (2008). The researchers also implemented constant step size in the proposed method and investigated the stability properties for the method to be more practical.

Khay et al. (2009) introduced GHI method with the implementation of constant step size presented as in the form of XX method. This approach is extended from the work in Khay and Chong (2007) in which it computed the solution at seven points concurrently by using six backward steps. The numerical results obtained have revealed that this method managed to give good results in solving general second order BDEs.

Sir, please help me check this text. Thanks a lot..

Mister Micawber · Answer

'Et al.' is common English and needn't be italicized. If you ever use the complete form (not here!), then it is uncommon and can be italicized: et alia.

Tau and Hu (2005) employed the ABC method based on the ZZ formula for solving higher-order BDEs directly. The authors designed the explicit method for computing solutions at seven points simultaneously using constant step size.

An implicit DEF method based on the YY formula for solving first-order DVPs was developed by Richard et al. (2008). The researchers also implemented constant step size in the proposed method and investigated the stability properties necessary for the method to be more practical.

Khay et al. (2009) introduced the GHI method with the implementation of constant step size as in the XX method. This approach is an extension of the work in Khay and Chong (2007) in which the solution is computed at seven points concurrently using six backward steps. This method produces satisfactory numerical results in solving general second-order BDEs.

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