Preface of the “Symposium on High Accuracy Solution of Ordinary and Partial Differential Equations”

It is feasible for the inverse problem of research in the very vital significance between in practical application. Genetic algorithm is applied in many aspects, but we are more concerned with the application in mathematics. From the start of genetic algorithm, the collection to search for comprehensive coverage of preferred. Due to genetic algorithm is used to search the information, and does not need such problems with the problem is directly related to the derivative of the information. Finally, the results of numerical simulation show that the GA method has high accuracy and quick convergent speed. And it is easy to program and calculate. It is worth of practical application.

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A new high accuracy two-level implicit off-step discretization for the system of two space dimensional quasi-linear parabolic partial differential equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2012.08.100 ◽

2012 ◽

Vol 219 (5) ◽

pp. 2680-2697 ◽

Cited By ~ 2

Author(s):

R.K. Mohanty ◽

Nikita Setia

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

High Accuracy ◽

Parabolic Partial Differential Equations ◽

Partial Differential

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High-accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations

Advances in Difference Equations ◽

10.1186/s13662-017-1274-3 ◽

2017 ◽

Vol 2017 (1) ◽

Cited By ~ 4

Author(s):

RK Mohanty ◽

Sachin Sharma

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

High Accuracy ◽

Parabolic Partial Differential Equations ◽

Partial Differential ◽

Variable Mesh ◽

Mesh Method ◽

Spline In Compression

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Applications of New Double Integral Transform (Laplace–Sumudu Transform) in Mathematical Physics

Abstract and Applied Analysis ◽

10.1155/2021/6625247 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Shams A. Ahmed

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Integral Transform ◽

Mathematical Physics ◽

High Accuracy ◽

Double Integral ◽

Partial Differential ◽

Fundamental Properties ◽

Sumudu Transform ◽

Basic Functions

The primary purpose of this research is to demonstrate an efficient replacement of double transform called the double Laplace–Sumudu transform (DLST) and prove some related theorems of the new double transform. Also, we will discuss the fundamental properties of the double Laplace–Sumudu transform of some basic functions. Then, by utilizing those outcomes, we will apply it to the partial differential equations to show its simplicity, efficiency, and high accuracy.

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Limitations due to Noise, Stability and Component Tolerance on the Solution of Partial Differential Equations by Differential Analysers

SIMULATION ◽

10.1177/003754976400300510 ◽

1964 ◽

Vol 3 (5) ◽

pp. 45-52 ◽

Cited By ~ 3

Author(s):

Michael E. Fisher

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Elliptic Equations ◽

Truncation Error ◽

High Accuracy ◽

Quantitative Investigation ◽

Parallel Method ◽

Partial Differential ◽

Truncation Errors ◽

The Difference

The solution of partial differential equations by a differential analyser is considered with regard to the effects of noise, computational instability and the deviation of components from their ideal values. It is shown that the 'serial' method of solving parabolic, hyperbolic and elliptic equations leads to serious in stability which increases as the finite difference interval is reduced. The truncation error (due to the difference approximations) decreases as the interval is made smaller and consequently an 'optimal' ac curacy is reached when the unstable noise errors match the truncation errors. Evaluation shows that the attainable accuracy is severely limited, especially for hyperbolic and elliptic equations. The 'parallel' method is stable when applied to parabolic and hyperbolic (but not elliptic) equations and the attainable accuracy is then limited by the accumulation of component tolerances. Quantitative investigation shows how reasonably high accuracy can be achieved with a minimum of precise adjustments.

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Numerical Analysis and Comparison of Gridless Partial Differential Equations

International Journal of Circuits, Systems and Signal Processing ◽

10.46300/9106.2021.15.133 ◽

2021 ◽

Vol 15 ◽

pp. 1223-1231

Author(s):

Zhao Zhang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Numerical Solution ◽

Numerical Solutions ◽

Absolute Error ◽

High Accuracy ◽

Science And Engineering ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Physical Phenomena

In the field of science and engineering, partial differential equations play an important role in the process of transforming physical phenomena into mathematical models. Therefore, it is very important to get a numerical solution with high accuracy. In solving linear partial differential equations, meshless solution is a very important method. Based on this, we propose the numerical solution analysis and comparison of meshless partial differential equations (PDEs). It is found that the interaction between the numerical solutions of gridless PDEs is better, and the absolute error and relative error are lower, which proves the superiority of the numerical solutions of gridless PDEs

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