Numerical relativity for ill-posed field equations in beyond-GR theories

Field equations in beyond-GR theories often have derivatives higher than order 2, typically from non-linear curvature terms in the action. PDEs with such higher-order derivatives are frequently ill-posed as initial-value problems. Accordingly, they cannot be solved numerically with the methods that have been so successful for GR. We introduce a novel approach to solving such problems using a Variational Iteration Method and demonstrate its effectiveness on a series of test problems.