Solving differential equations

[vmakarichev]

Hi everyone! Explore Diff Studio, Datagrok tool for solving differential equations.

[vmakarichev]

Diff Studio takes a set of the differential equations in a declarative form, and creates a UI that solves the equations, visualizes the results, and lets you change parameters on the fly.

[vmakarichev]

Diff Studio has built-in examples. They cover all Diff Studio capabilities. Use them them as a template.

[vmakarichev]

In Diff Studio, you get interactive model exploration. Use annotating to customize interface.

[vmakarichev]

Diff Studio has built-in sensitivity analysis feature. Run it to analyze the relationship between inputs and outputs of your model.

[vmakarichev]

In Diff Studio, you can find input conditions leading to the specified output constraints for several clicks. Use the parameter optimization feature.

[vmakarichev]

Diff Studio 1.1.1

Meet the new version of Diff Studio. This release provides:

• 64-bit floats usage
  • higher precision
  • removal of numerical artifacts
• Integration to the browse tree
  • check models from the Templates & Examples folders
  • find recent models in the Recent folder
• Templates & Examples update
  • use the improved templates as a backbone of your project
  • explore the Pollution model

Check it!

[vmakarichev]

Browse

Go to Browse > Apps and expand the Diff Studio group:

• Check model templates from Templates. Start creating your project using them.

• Click Examples and explore built-in models. These recipes cover all Diff Studio capabilities.

• Find recently opened models in Recent.

[vmakarichev]

Share

Use URL to share models and their particular runs. Apply this feature to any item from Templates, Examples and Recent groups. Also, you can share models stored in ivp-files:

[vmakarichev]

Performance

Diff Studio ensures solving both stiff and non-stiff equations.

Go to Browse > Apps > Diff Studio > Examples and select Pollution. This example describes a chemical reaction part of the air pollution model. This model consists of 25 reaction and 20 reacting compounds:

Move sliders and explore this model:

[vmakarichev]

Benchmarks

Diff Studio implements the following Rosenbrock–Wanner methods: the modified Rosenbrock triple (MRT), ROS3PRw and ROS34PRw. They provide fast in-browser solving ODEs.

Check benchmarks:

Problem	Segment	Points	Tolerance	MRT, ms	ROS3PRw, ms	ROS34PRw, ms
Rober	[0, 10E+11]	40K	1E-7	125	1066	507
HIRES	[0, 321.8122]	32K	1E-10	626	931	489
VDPOL	[0, 2000]	20K	1E-12	1124	2884	904
OREGO	[0, 360]	36K	1E-8	947	1131	440
E5	[0, 10E+13]	40K	1E-6	24	52	18
Pollution	[0, 60]	30K	1E-6	71	139	32

Here, the following classic problems are presented:

• Rober
  • a stiff system of 3 nonlinear ODEs
  • describes the kinetics of an autocatalytic reaction given by Robertson
• HIRES
  • a stiff system of 8 non-linear equations
  • explains the `High Irradiance Responses’ (HIRES) of photomorphogenesis on the basis of phytochrome, by means of a chemical reaction involving eight reactants
• VDPOL
  • a system of 2 ODEs proposed by B. van der Pol
  • describes the behaviour of nonlinear vacuum tube circuits
• OREGO
  • a stiff system of 3 non-linear equations
  • simulates Belousov-Zhabotinskii reaction
• E5
  • a stiff system of 4 non-linear ODEs
  • represents a chemical pyrolysis model
• Pollution
  • a stiff system of 20 non-linear equations
  • describes a chemical reaction part of the air pollution model designed at The Dutch National Institute of Public Health and Environmental Protection

[vmakarichev]

Lookup tables

Apply lookup tables in your model. They let you initialize its inputs with a set of pre-defined values. To switch between input sets, it only takes a couple of clicks:

Run the Bioreactor example and check this feature.

[vmakarichev]

The use of lookup tables reduces your job, when applying sensitivity analysis and parameter optimization. Switch between input sets in a few clicks:

Run the Bioreactor example and check this feature.