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Showing 1 to 4 of 4 for “"General Linear Methods"”.
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The analysis and implementation of exponential almost Runge-Kutta methods for semilinear problems
… the multi-step Exponential Time Differencing Methods and the multi-stage Exponential Runge-Kutta Methods. A broader framework of Exponential General Linear Methods builds on these two families. We extend the classical Almost Runge-Kutta Method family, of multi-stage multi-value schemes, into …
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Multimethods for the Efficient Solution of Multiscale Differential Equations
… Advances in computing hardware and numerical methods have allowed these models to become larger and more sophisticated. Increasingly, problems can be described as multiphysics and multiscale as they combine several different physical processes with different characteristics. If just one part …
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Efficient Time Stepping Methods and Sensitivity Analysis for Large Scale Systems of Differential Equations
… the creation of new families of time integration methods for multiscale and multiphysics simulations, and the development of industrial-strengh tools for sensitivity analysis. This work develops novel implicit-explicit (IMEX) general linear time integration methods for multiphysics and multiscale …
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Polynomial-Based Methods for Time-Integration
… framework. Both parts discuss time integration methods that can be derived without solving nonlinear order conditions. In part I, we introduce a time-integration framework for solving systems of first-order ordinary differential equations by using interpolating polynomials. Our approach is to …