VisualPDE: rapid interactive simulations of partial differential equations Article Swipe
Benjamin J. Walker
,
Adam K. Townsend
,
Alexander K. Chudasama
,
Andrew L. Krause
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2308.01245
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2308.01245
Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise solutions in different ways. Using ubiquitous computing infrastructure, we provide a means to go one step further in using computers to understand complex models through instantaneous and interactive exploration. This ubiquitous infrastructure has enormous potential in education, outreach and research. Here, we present VisualPDE, an online, interactive solver for a broad class of 1D and 2D partial differential equation (PDE) systems. Abstract dynamical systems concepts such as symmetry-breaking instabilities, subcritical bifurcations and the role of initial data in multistable nonlinear models become much more intuitive when you can play with these models yourself, and immediately answer questions about how the system responds to changes in parameters, initial conditions, boundary conditions or even spatiotemporal forcing. Importantly, VisualPDE is freely available, open source and highly customisable. We give several examples in teaching, research and knowledge exchange, providing high-level discussions of how it may be employed in different settings. This includes designing web-based course materials structured around interactive simulations, or easily crafting specific simulations that can be shared with students or collaborators via a simple URL. We envisage VisualPDE becoming an invaluable resource for teaching and research in mathematical biology and beyond. We also hope that it inspires other efforts to make mathematics more interactive and accessible.
Related Topics
Concepts
Computer science
Solver
Forcing (mathematics)
Dynamical systems theory
Partial differential equation
Class (philosophy)
Nonlinear system
Outreach
Simple (philosophy)
Resource (disambiguation)
Theoretical computer science
Data science
Mathematics
Artificial intelligence
Physics
Programming language
Philosophy
Epistemology
Computer network
Political science
Mathematical analysis
Quantum mechanics
Law
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2308.01245
- https://arxiv.org/pdf/2308.01245
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4385969813
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W4385969813Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2308.01245Digital Object Identifier
- Title
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VisualPDE: rapid interactive simulations of partial differential equationsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-08-02Full publication date if available
- Authors
-
Benjamin J. Walker, Adam K. Townsend, Alexander K. Chudasama, Andrew L. KrauseList of authors in order
- Landing page
-
https://arxiv.org/abs/2308.01245Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2308.01245Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2308.01245Direct OA link when available
- Concepts
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Computer science, Solver, Forcing (mathematics), Dynamical systems theory, Partial differential equation, Class (philosophy), Nonlinear system, Outreach, Simple (philosophy), Resource (disambiguation), Theoretical computer science, Data science, Mathematics, Artificial intelligence, Physics, Programming language, Philosophy, Epistemology, Computer network, Political science, Mathematical analysis, Quantum mechanics, LawTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
- Citations by year (recent)
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2023: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.designing | 172 |
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| institutions_distinct_count | 4 |
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