Teaching Modeling with Partial Differential Equations: Several Successful Approaches

Myers, J.; Trubatch, David; Winkel, Brian

doi:10.1080/10511970701643889

Cited by 2 publications

(4 citation statements)

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“…In the teaching arena, the visualization of PDE models can help students in the learning process, as they typically get lost in the technical features of the analytical solutions of the equations. Moreover, as these solutions are functions, sometimes depending on a time variable, a dynamic plot represents a qualitative change of conception for them (Myers et al, 2008;VTK, 2016).…”

Section: Introductionmentioning

confidence: 99%

Simulation of partial differential equations models in Java

Caño

Chacon-Vera

Esquembre

2017

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Purpose Computer simulations improve the knowledge of physical models and are widely used in teaching and research. Key aspects are to understand their solutions and to make interactive changes to the models, observing their effects in real-time. The drawback of creating interactive simulations of physical models is the high level of programming expertise required. The purpose of this study is to facilitate this task. Design/methodology/approach Java is the perfect language for this task; it yields high-quality graphics and is widely spread in the scientific community. Because many important physical models are described by means of partial differential equations (PDEs), the combination of Java with FreeFem++, a C++ PDE solver based on the finite element method, is considered. Findings In this study, a Java library is introduced to numerically solve PDE equations via a run-time connection with FreeFem++. The solution is encapsulated into Java objects that are ready to be used in different programming tasks. The library also includes new Java visualization elements for solutions and meshes in the context of the Open Source Physics project library. Together, the connection features and the visualization elements facilitate the creation of Java simulations by programming researchers. For those with less programming capabilities, this work has been included into Easy Java Simulations, a tool to further ease the creation of interactive simulations. Originality/value The present study approach allows simulating models given PDEs. The equations are solved either in local or in remote mode (e.g. by a network accessible to a high-performance computer) and visualized locally, providing a high degree of interactivity to the end user.

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Section: Introductionmentioning

confidence: 99%

Simulation of partial differential equations models in Java

Caño

Chacon-Vera

Esquembre

2017

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“…• The equations are intrinsically a complicated matter and it is not simple to handle an easy introduction to the field [15]. • A typical approach to this field leads to the analytic solution of the basic transport, diffusion and wave equations with constant coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…• A common strategy is the separation of variables method which requires some knowledge of Fourier series. This adds more noise to the picture [15]. • Solutions are not numbers but functions, a conceptual jump for students that is better understood by using graphical visualizations [18].…”

Section: Introductionmentioning

confidence: 99%

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Bringing partial differential equations to life for students

Caño¹,

Chacon-Vera²,

Esquembre³

2015

Eur. J. Phys.

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Teaching partial differential equations (PDEs) carries inherent difficulties that an interactive visualization might help overcome in an active learning process. However, the generation of this kind of teaching material implies serious difficulties, mainly in terms of coding efforts. This work describes how to use an authoring tool, Easy Java Simulations, to build interactive simulations using FreeFem++ (Hecht F 2012 J. Numer. Math. 20 251) as a PDE solver engine. It makes possible to build simulations where students can change parameters, the geometry and the equations themselves getting an immediate feedback. But it is also possible for them to edit the simulations to set deeper changes. The process is ilustrated with some basic examples. These simulations show PDEs in a pedagogic manner and can be tuned by no experts in the field, teachers or students. Finally, we report a classroom experience and a survey from the third year students in the Degree of Mathematics at the University of Murcia.

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Teaching Modeling with Partial Differential Equations: Several Successful Approaches

Cited by 2 publications

References 1 publication

Simulation of partial differential equations models in Java

Simulation of partial differential equations models in Java

Bringing partial differential equations to life for students

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