Study on Accurate Symbolic Solution of Ginzburg-Landau Equations in the Circular Cell Approximation by Variational Method: An Approach towards Magnetization of Ideal Type II Superconductor

Abstract

This chapter examines the degree of approximation of the well-known symbolic technique to solving Ginzburg-Landau (GL) equations using the variational method and the concept of a vortex lattice with circular unit cells, refines it in a clear and straightforward manner, and finds and eliminates flaws. I will enhance the accuracy by offering for the first time precise dependencies of the variational characteristics; correct and calculate magnetization, start comparing it to the one calculated mathematically, and reach the conclusion that they agree within 98.5 percent or better for any value of the GL parameter k and at magnetic field 0.01 \(\le\) \(\bar{B}\) /B_c2 \(\le\) 1, which is a great foundation for many engineering disciplines.  As an outcome, a theoretical tool based on known symbolic solutions to GL equations has been built, with precision exceeding any previous known symbolic solution and approaching numerical accuracy.