image thumbnail

Linear differential equation solver (lde.m)

version 1.6.1 (192 KB) by Kenneth Johnson
solves a linear, first-order, vector differential equation


Updated 15 Jun 2021

View License

lde.m solves linear, vector differential equations, including nonhomogeneous equations with functional coefficients. For a constant square matrix A, lde(A) is functionally equivalent to expm(A) (exponential matrix), although lde can be faster (for large matrices) and can exhibit better numerical accuracy (e.g. by a factor of 10^-15 in one test case). Relative to MATLAB's ordinary differential solvers (e.g. ode45), an advantage of lde is that it can simultaneously obtain all independent solutions of a homogeneous differential equation, or can simultaneously process multiple forcing functions for a nonhomogeneous equation. A live script demo is included showing several practical applications: (1) exponential matrix, (2) resonantly forced harmonic oscillator, (3) harmonic oscillator with variable mass ("leaky bucket on a spring"), (4) Airy functions, and (5) Scorer functions.

Cite As

Kenneth Johnson (2022). Linear differential equation solver (lde.m) (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2016b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!