Stephen Ehidiamhen Uwamusi

Numerical Computation of Cauchy’s Integral Theorem for Matrix Function

Cauchy’s integral theorem for the matrix function is studied. Using the iteration formula of the Runge–Kutta fourth-order method, we advance the solution to Cauchy’s integral theorem, wherein Jacobi elliptic integrals and the Mobius transformation are applicable. It is proven that the method converges uniformly locally on the solid triangle.  The hyperbolic matrix tangent in the arc length when the contour winds once counterclockwise around the integral is computed. Numerical results have been reported with great success.

By admin, 26 November, 2024

Thickening annulus in Cauchy’s integral Theorem for matrix function with Mobius Transformation via Trapezoidal rule and Runge-Kutta fourth –order method

This study discusses thickening annulus in Cauchy’s integral theorem for matrix function via Mobius transformation. We introduce a Jacobi type elliptic integral for arc length using Mobius transformation leading to optimization in the contour integral wherein Trapezoidal rule and Runge-Kutta fourth order method are used yielding approximate solutions to the integral problem. We filtered out noise from solution space using Tikhonov regularization method. This leads to computing for the path integral, path length and size of the path for the Cauchy integral.

Stephen Ehidiamhen Uwamusi