Add to ORKGiv Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential equation. Several examples are presented. v v
Despite their central place in mathematical physics, Lie groups are generally regarded as requiring ...
Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the...
In this paper Lie group theory is used to reduce the order of ordinary differential equations. For a...
Differential equations are vitally important in numerous scientific fields. Oftentimes, they are qui...
Differential equations have bearing on practically every scientific field. Though they are prevalent...
Differential equations have bearing on practically every scientific field. Though they are prevalent...
Differential equations have bearing on practically every scientific field. Though they are prevalent...
In the late nineteenth century, Sophius Lie developed a technique to solve differential equations us...
In this paper Lie group theory is used to reduce the order of ordinary differential equations. For a...
Most well-known solution techniques for differential equations exploit symmetry in some form. System...
Most well-known solution techniques for differential equations exploit symmetry in some form. System...
This article reviews the use of differential forms and Lie derivatives to find symmetries of differe...
Most well-known solution techniques for differential equations exploit symmetry in some form. System...
Present differential equations solver are often based on a list of equations the so-lutions of which...
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonli...
Despite their central place in mathematical physics, Lie groups are generally regarded as requiring ...
Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the...
In this paper Lie group theory is used to reduce the order of ordinary differential equations. For a...
Differential equations are vitally important in numerous scientific fields. Oftentimes, they are qui...
Differential equations have bearing on practically every scientific field. Though they are prevalent...
Differential equations have bearing on practically every scientific field. Though they are prevalent...
Differential equations have bearing on practically every scientific field. Though they are prevalent...
In the late nineteenth century, Sophius Lie developed a technique to solve differential equations us...
In this paper Lie group theory is used to reduce the order of ordinary differential equations. For a...
Most well-known solution techniques for differential equations exploit symmetry in some form. System...
Most well-known solution techniques for differential equations exploit symmetry in some form. System...
This article reviews the use of differential forms and Lie derivatives to find symmetries of differe...
Most well-known solution techniques for differential equations exploit symmetry in some form. System...
Present differential equations solver are often based on a list of equations the so-lutions of which...
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonli...
Despite their central place in mathematical physics, Lie groups are generally regarded as requiring ...
Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the...
In this paper Lie group theory is used to reduce the order of ordinary differential equations. For a...