Journal
2014 INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE
Volume 29, Issue -, Pages 1014-1026Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.procs.2014.05.091
Keywords
PDEs; stiff ODEs; Backward Differentiation Formula; adaptive BDF2
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Funding
- Basque Government Consolidated Research Group [IT649-13]
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After applying the Finite Element Method (FEM) to the diffusion-type and wave-type Partial Differential Equations (PDEs), a first order and a second order Ordinary Differential Equation (ODE) systems are obtained respectively. These ODE systems usually present high stiffness, so numerical methods with good stability properties are required in their resolution. MATLAB offers a set of open source adaptive step functions for solving ODEs. One of these functions is the ode15s recommended to solve stiff problems and which is based on the Backward Differentiation Formulae (BDF). We describe the error estimation and the step size control implemented in this function. The ode15s is a variable order algorithm, and even though it has an adaptive step size implementation, the advancing formula and the local error estimation that uses correspond to the constant step size formula. We have focused on the second order accurate and unconditionally stable BDF (BDF2) and we have implemented a real adaptive step size BDF2 algorithm using the same strategy as the BDF2 implemented in the ode15s, resulting the new algorithm more efficient than the one implemented in MATLAB.
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