{"id":22462569,"url":"https://github.com/louis-finegan/second-order-ode","last_synced_at":"2026-05-09T05:31:26.471Z","repository":{"id":166016408,"uuid":"598630727","full_name":"Louis-Finegan/Second-Order-ODE","owner":"Louis-Finegan","description":"Solving second order ODEs and Systems of ODEs with scipy library.","archived":false,"fork":false,"pushed_at":"2023-11-21T11:44:54.000Z","size":693,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-02-01T18:36:35.142Z","etag":null,"topics":["calculus","eigenvalues","equilibrium-point","matplotlib","numerical-integration","numpy","ordinary-differential-equations","python","python3","scipy"],"latest_commit_sha":null,"homepage":"https://github.com/Louis-Finegan/Second-Order-ODE","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/Louis-Finegan.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2023-02-07T14:01:37.000Z","updated_at":"2024-10-28T07:03:39.000Z","dependencies_parsed_at":"2023-11-21T12:50:35.223Z","dependency_job_id":null,"html_url":"https://github.com/Louis-Finegan/Second-Order-ODE","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Louis-Finegan%2FSecond-Order-ODE","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Louis-Finegan%2FSecond-Order-ODE/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Louis-Finegan%2FSecond-Order-ODE/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Louis-Finegan%2FSecond-Order-ODE/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/Louis-Finegan","download_url":"https://codeload.github.com/Louis-Finegan/Second-Order-ODE/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":245858889,"owners_count":20684062,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["calculus","eigenvalues","equilibrium-point","matplotlib","numerical-integration","numpy","ordinary-differential-equations","python","python3","scipy"],"created_at":"2024-12-06T09:10:12.524Z","updated_at":"2025-10-25T18:05:14.803Z","avatar_url":"https://github.com/Louis-Finegan.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Second Order ODEs and Systems of ODEs with `SciPy`\n\n## Solves a second order Linear ODE \n\nTakes the form:\n\n$$\\frac{d^2y}{dt^2} + a(t)\\frac{dy}{dt} + b(t)y = c(t)$$\n\nWith initial conditions $y(0) = y_0$ and $y^\\prime(0) = y^\\prime_0$.\n\nCoefficients are functions of $t$ and are defined in `second_order.ipynb`\n\n`second_order_ode` module in the `solve.py` file in the `ode` directory, and is imported into `second_order.ipynb`.\n\n## Solves a First Order System of ODEs\n\nTakes the form:\n\n$$\\frac{dx}{dt} = F(x, y)$$\n\n$$\\frac{dy}{dt} = G(x, y)$$\n\nWith initial conditions $x(0) = x_0$ and $y(0) = y_0$.\n\n$F$ and $G$ are defined in `first_order_system.ipynb`.\n\n`first_order_system_2vars` module in the `solve.py` file in the `ode` directory, and is imported into `first_order_system.ipynb`.\n\nThen for 3 variable systems, use the module `first_order_system_3vars`.\n \n## Required packages and libaries\n\n1. `numpy`\n\n2. `scipy` using the `integrate` module \n\n3. `scipy` using the `optimize` module \n\n3. `matplotlib` using the `pyplot` module\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Flouis-finegan%2Fsecond-order-ode","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Flouis-finegan%2Fsecond-order-ode","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Flouis-finegan%2Fsecond-order-ode/lists"}