Abstract
Numerical solution of parabolic differential equations using finite differences: a comparative study
Highlights
The modeling of many problems related to several areas of knowledge, such as Physics, Biology, Economics, Engineering and Geometry has resulted in complex equations
The Von Neumann criterion is widely used to determine the stability of a finite difference method
=0 in that is the global error at each poin√t along the line, = is the wave number in the direction of, is the length of the x-axis, = −1, n is the amplitude in the time axis in n, is a complex number and h =
Summary
The modeling of many problems related to several areas of knowledge, such as Physics, Biology, Economics, Engineering and Geometry has resulted in complex equations. From the effort of great mathematicians, many important contributions to the solution of these problems have arisen. Many researchers are currently working on finding solution methods. With the great evolution of computing, enormously increasing the capacity of data processing, the computer has become a very powerful tool for the solution of these equations and the problems mentioned. Studies of physical phenomena and nature were based on two scientific methods: theoretical and practical. The theoretical method develops principles, laws, equations, and physical theories of problems. Scientific studies have benefited enormously from the technological advances and connected the practical and theoretical methods, being able to work with a new method: the numerical one
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