An explicit Jacobian for Newton's method applied to nonlinear initial boundary value problems in summation-by-parts form

• Published in: AIMS mathematics Vol. 9; no. 9; pp. 23291 - 23312
• Main Authors: Nordström, Jan, Laurén, Fredrik, Ålund, Oskar
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: incompressible Navier-Stokes equations; Jacobian; Newton's method; nonlinear initial boundary value problems; summation-by-parts; weak boundary conditions

We derived an explicit form of the Jacobian for discrete approximations of a nonlinear initial boundary value problems (IBVPs) in matrix-vector form. The Jacobian is used in Newton's method to solve the corresponding nonlinear system of equations. The technique was exemplified on the incompress...