The Application of Sparse Matrix Methods to the Numerical Solution of Nonlinear Elliptic Partial Differential Equations.
YALE UNIV NEW HAVEN CONN DEPT OF COMPUTER SCIENCE
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The authors present a new algorithm for solving general semilinear, elliptic partial differential equations. The algorithm is based on Newtons Method but uses an approximate iterative method to solve the linear systems that arise at each step of Newtons Method. The authors show that the algorithm can maintain the quadratic convergence of Newtons Method and that it may be substantially faster than other available methods for semilinear or nonlinear partial differential equations.
- Numerical Mathematics