Crank Nicolson implicit method from new version

[Longyu975]

Implemented the Crank-Nicolson implicit method to improve energy conservation
Added substepping and LAX scan to reduce runtime.
Adjusted input parameters for Landau damping

[codecov]

Codecov Report

Attention: Patch coverage is 38.18182% with 68 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
jaxincell/_algorithms.py	35.35%	63 Missing and 1 partial ⚠️
jaxincell/_simulation.py	70.00%	2 Missing and 1 partial ⚠️
jaxincell/_plot.py	0.00%	1 Missing ⚠️

Files with missing lines	Coverage Δ
jaxincell/_diagnostics.py	100.00% <ø> (ø)
jaxincell/_plot.py	5.84% <0.00%> (ø)
jaxincell/_simulation.py	88.40% <70.00%> (-0.84%)	⬇️
jaxincell/_algorithms.py	35.35% <35.35%> (ø)

[Copilot]

Pull Request Overview

This PR implements an implicit Crank-Nicolson time evolution method with Picard iterations and particle substepping to improve energy conservation and streamline runtime. Key changes include adding CN_step and its supporting parameters to the simulation workflow, updating the simulation function to select between Boris and implicit methods based on a new parameter, and modifying example inputs to use the implicit scheme.

Reviewed Changes

Copilot reviewed 4 out of 5 changed files in this pull request and generated 1 comment.

File	Description
jaxincell/_simulation.py	Adds new parameters and branches to support implicit Crank-Nicolson via CN_step
jaxincell/_algorithms.py	Introduces the CN_step function with Picard iterations and substepping logic
examples/Landau_damping.py	Updates simulation and solver parameters to employ the implicit time evolution algorithm
example_input.toml	Adjusts solver parameters and total steps to reflect the new implicit method configuration

Comments suppressed due to low confidence (1)

jaxincell/_simulation.py:138

• Please update the function docstring to document the newly added parameters 'number_of_Picard_iterations_implicit_CN' and 'number_of_particle_substeps_implicit_CN' for better clarity.

                                ,number_of_Picard_iterations_implicit_CN=7, number_of_particle_substeps_implicit_CN=2):

[rogeriojorge]

Code looks good, except the new variable names for the inputs that include _x, _y or _z. I'll run the new code and benchmarks later to make sure the results are the same.