Unconditionally Stable Linearly Implicit Schemes for Gradient Systems with Quartic Potentials

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The discrete gradient method is one of the most prevalent approaches for deriving structure-preserving numerical schemes for dissipative and conservative gradient systems. Using a regularized energy relaxation technique, the theory of polar forms and the discrete gradient method, we derive conditions on the regularization ensuring the unconditional stability of the resulting linearly implicit schemes for dissipative gradient systems with quartic potentials. Moreover, we show that for conservative systems, unconditional stability can be achieved without regularization. Joint work with Rachid Ait Haddou.

Brief Biography

Safiya Alshehaiween is currently a Ph.D. student in Mathematics at King Fahd University of Petroleum and Minerals. Her general interest lies in the area of Applied Mathematics and its interaction with Biology and Medical sciences.