Time-adaptive GWRM Lorenz 1984

The Generalized Weighted Residual Method, being a time-spectral algorithm, seeks to increase the time intervals in the computation without degrading the efficiency, accuracy, and stability. It does this by postulating a solution ansatz as a sum of weighted Chebyshev polynomials, in combination with the Galerkin method, to create a set of linear/non-linear algebraic equations. These algebraic equations are then solved iteratively using a Semi Implicit Root solver (SIR), which has been chosen due to its enhanced global convergence properties. Furthermore, to achieve a desired accuracy across the entire domain, a time-adaptive algorithm has been developed. By evaluating the magnitudes of the Chebyshev coefficients in the time dimension of the solution ansatz, the time interval can either be decreased or increased.

广义加权残差法，作为一种时频算法，旨在在不降低效率、准确性和稳定性的前提下，延长计算的时间间隔。该算法通过假设解的形式为加权切比雪夫多项式的和，并结合伽辽金方法，构建一组线性/非线性代数方程。随后，这些代数方程通过半隐式根求解器（SIR）进行迭代求解，选择SIR的原因在于其卓越的全局收敛特性。此外，为了在整个域内达到所需的精度，还开发了一种时间自适应算法。通过评估解的假设中切比雪夫系数在时间维度上的幅度，时间间隔可以被相应地减小或增大。