On the integral solution of the one-dimensional Bratu problem

作者：Mohsen A^*

来源：Journal of Computational and Applied Mathematics, 2013, 251: 61-66.

DOI：10.1016/j.cam.2013.03.024

• Bratu%26apos
• s problem
• Green%26apos
• s functions
• Integral equations
• Nonlinear conjugate-gradient
• Rod buckling problem
• Troesch problem

A brief survey of the properties and different treatments of the one-dimensional (1D) planar Bratu problem is presented. The treatment using Green%26apos;s function is considered. Different iterative treatments of the resulting nonlinear system of equations are discussed. Starting the solution with simple sinusoidal function having appropriate amplitude is recommended. Then the resulting system is solved using a nonlinear conjugate-gradient (NL-CG) method. The importance of the proper choice of the starting function as well as the stopping criterion of the iterative solution are stressed.

• 出版日期2013-10-15