Moving Node Method for the Approximate Analytical Solution One-dimensional Convection-Diffusion Problems| Chapter 4 | Novel Research Aspects in Mathematical and Computer Science Vol. 7

 The following four groups of approaches can be used to solve mathematical physics problems.

Analytical procedures, such as the method of characteristics, the method of Green's functions, etc., have a relatively low degree of universality and are therefore concentrated on resolving relatively small classes of issues.

Analytical methods are less ubiquitous than approximate analytical methods, which include projection, variational methods, small parameter methods, operational methods, and different iterative methods.

Numerical techniques, such as the finite difference method, method of lines, control volume technique, and finite element technique, are extremely versatile techniques.

Monte Carlo methods, often known as probabilistic approaches, are quite flexible. Calculations for discontinuous solutions are possible. However, when solving such issues to which these approaches are suitable, they necessitate a lot of calculations and typically fall short of the computational complexity of the above methods. This chapter discusses novel methods for resolving boundary value issues in differential equations. It brings a fresh approach to node movement. Analytical solutions that are roughly accurate are produced by approximating differential equations (using the finite difference approach or the control volume method) and incorporating the idea of a moving node. Multipoint moving nodes are employed to improve the accuracy of the analytical answers that are obtained. Compact circuits are built using the moving node technique. You can examine the monotonicity of the diskette equation and the differential equation's approximation error using the moving node approach. Different test issues are taken into account. Mathematical subjects.

Author(s) Details:

Dalabaev Umurdin,
Department of Mathematics Modeling and Informatics, University of World Economy and Diplomacy, Tashkent, Uzbekistan.

Ikramova Malika,
Scientific Research Institute of Irrigation and Water Problems, Uzbekistan.

Umarova Shoira,
Department of Mathematics Modeling and Informatics, University of World Economy and Diplomacy, Tashkent,

Uzbekistan.

Please see the link here: https://stm.bookpi.org/NRAMCS-V7/article/view/7949