The New Way to Solve Physical Problems Described by ODE of the Second Order with the Special Structure

Ibrahimov, Vagif; Imanova, Mehriban

doi:10.37394/23202.2023.22.20

Cited by 4 publications

(2 citation statements)

References 31 publications

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“…Noted that for this aim, here can be recommending the following hybrid methods: . These methods usually give the best results [42][43][44][45][46][47][48][49][50][51].…”

Section: Numerical Resultsmentioning

confidence: 99%

About Some Applications Multistep Methods with Constant Coefficients to Investigation of Some Biological Problems

2023

AJBSR

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In our life we very often meet with mathematical models for which are described by using Ordinary Differential Equations. These equations are studied starting from the epoch of Newton. Therefore, many scientists believe that it is impossible to find something new in this area. However, it is not. We will show that in this area one can construct numerical methods for solving these equations, which have some advantages. Here it has been shown that it is possible to construct a stable method having a higher order of accuracy than the known. For this here is suggested to use the multistep methods having the advanced and hybrid types. To consider the construction of methods with new properties on the intersection of the above mentioned. methods. As is known, models for much biological research are described by the ordinary Differential equation, and the methods studied here can be applied to solving above mentioned problems. Therefore, here found the maximum value for the order of accuracy of the stable methods having the advanced and hybrid types. And considered to define the maximum value for the stable methods constructed on the intersection of these methods. By the application some of specific methods to solve model problems, have demonstrated the advantages of the proposed methods. By considering that in the investigation of multistep methods one of the basic questions is the determine the necessary condition of its convergence, here have defined the conditions, which are imposed on the coefficients investigated methods. For obtaining reliable information on the solution of the problem under study suggested to use the bilateral methods. For the illustration of this have constructed simple bilateral stable methods, which have applied to solve model problems. And, given a sequence studying the conception of stability for multistep methods in terms of history. The receiving results here are illustrated on solving some model problems, with the methods suggested here.

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“…Noted that for this aim, here can be recommending the following hybrid methods: . These methods usually give the best results [42][43][44][45][46][47][48][49][50][51].…”

Section: Numerical Resultsmentioning

confidence: 99%

About Some Applications Multistep Methods with Constant Coefficients to Investigation of Some Biological Problems

2023

AJBSR

View full text Add to dashboard Cite

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“…When comparing identities (11)(12)(13)(14), the HMs type is considered the best among MSMs. Some of the weaknesses of these methods can be found in [18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Construction Pcms By Using the Known Simple Methodsmentioning

confidence: 99%

On Some Advantages of the Predictor-Corrector Methods

Ibrahimov,

Yue,

Juraev

2023

IETI Trans. Data Anal. Forecast.

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Usually, all numerical methods are divided into two sets known as explicit and implicit methods. Explicit methods (EM) are used to find a solution to a problem directly, without requiring initial preparation. But when using the implicit method (IM), other methods can sometimes be employed. Implicit methods are known to be more accurate than explicit ones. Therefore, the question arises about finding the golden mean. To accomplish this, we utilize certain properties of the predictor and corrector methods. We take into account that in forecasting methods, we use EM. However, I will show here that in some cases, IMs can be used as correction methods. It is clear that the results obtained here are fully consistent with the theoretical ones. To address the aforementioned issues, we employ the initial value problem (IVP) for a first-order ordinary differential equation (ODE). Conventional methods compare various nanomaterials (NMs) using multi-step, extended, and hybrid approaches.

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On Some Ways to Increase the Exactness of the Calculating Values of the Required Solutions for Some Mathematical Problems

Imanova,

Ibrahimov

2024

Wseas Transactions on Mathematics

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The expansion of the application of computational methods for solving many mathematical problems from various fields of natural knowledge does not raise any doubts. One of the promising directions in contemporary sciences is considered to be in areas that are at the intersection of different sciences. Solving such problems is more difficult because different laws from different areas are used. It should be noted that at the intersection of these sciences, there are problems, which can come down to solving ordinary differential equations. Therefore, studies of differential equations have always been considered promising. Based on this, the application of some methods for solving initial problems for first-order ODEs is investigated. For this purpose, scientists studied a numerical solution to the initial problem of the ODE. Here, we have reviewed the study of linear Multistep Methods with constant coefficients. With its help, the order of accuracy of the calculated values is determined. In addition, determines how much accuracy values increase when using Richardson extrapolation methods and also when using linear combinations of various methods. To construct an innovative method is proposed here using advanced methods. It is shown that using these methods it is possible that A-stable methods can be taken as innovative.

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The New Way to Solve Physical Problems Described by ODE of the Second Order with the Special Structure

Cited by 4 publications

References 31 publications

About Some Applications Multistep Methods with Constant Coefficients to Investigation of Some Biological Problems

About Some Applications Multistep Methods with Constant Coefficients to Investigation of Some Biological Problems

On Some Advantages of the Predictor-Corrector Methods

On Some Ways to Increase the Exactness of the Calculating Values of the Required Solutions for Some Mathematical Problems

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