High precision multi-step particle-in-cell algorithm with explicit prediction and implicit correction

This repository contains MATLAB scripts and associated data needed for single-particle PIC (Particle-In-Cell) benchmarks, as well as two additional tests (two-stream instability and Landau damping). Single-Particle Tests: High-Precision Multi-Step Particle-In-Cell (MSPIC.m) Boris Algorithm (Boris.m) Direct Implicit Algorithm (DirectIm.m) Each script computes the time evolution of particle position, velocity, and energy. You may customize parameters such as time-step size, grid resolution, and electromagnetic field configurations. Two-Stream Instability Test: A benchmark script demonstrating two-stream instability using the MSPIC approach. Landau Damping Test: A benchmark script illustrating Landau damping under the MSPIC approach.本仓库包含用于单粒子PIC（Particle-In-Cell）基准测试所需的MATLAB脚本及配套数据，同时附带两项额外测试：双流不稳定性测试与朗道阻尼测试。 单粒子测试包含以下三项： 高精度多步粒子网格算法（MSPIC.m）、鲍里斯算法（Boris.m）以及直接隐式算法（DirectIm.m）。 各脚本均可计算粒子位置、速度与能量的时间演化过程，用户可自定义时间步长、网格分辨率以及电磁场配置等参数。 双流不稳定性测试：采用MSPIC方法演示双流不稳定性现象的基准测试脚本。 朗道阻尼测试：采用MSPIC方法展示朗道阻尼现象的基准测试脚本。