{"entities":{"Q1680":{"pageid":3326,"ns":120,"title":"Item:Q1680","lastrevid":7377,"modified":"2026-09-04T07:28:21Z","type":"item","id":"Q1680","labels":{"en":{"language":"en","value":"Euler's method in Python"}},"descriptions":{},"aliases":{},"claims":{"P1":[{"mainsnak":{"snaktype":"value","property":"P1","hash":"dad80ce021597708e456b39bc26c8f08f3771429","datavalue":{"value":{"entity-type":"item","numeric-id":3,"id":"Q3"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q1680$287D2E88-7B3B-4236-8CD0-FFACAE2BC8AE","rank":"normal"}],"P3":[{"mainsnak":{"snaktype":"value","property":"P3","hash":"483ff5eb5096c7822b6f7f20a8fa72bf64096558","datavalue":{"value":"def euler(f, x0, y0, h, n):\\n    \"\"\"Advance y' = f(x, y), y(x0) = y0 by n Euler steps of size h.\"\"\"\\n    xs, ys = [x0], [y0]\\n    x, y = x0, y0\\n    for _ in range(n):\\n        y = y + h * f(x, y)\\n        x = x + h\\n        xs.append(x)\\n        ys.append(y)\\n    return xs, ys\\n\\n# y' = y, y(0) = 1, ten steps of h = 0.1 on [0, 1]; exact value e\\nxs, ys = euler(lambda x, y: y, 0.0, 1.0, 0.1, 10)\\nprint(ys[-1])  # 2.5937424601... versus e = 2.718281828...","type":"string"},"datatype":"string"},"type":"statement","id":"Q1680$368D6979-B749-4DDE-8657-1BE77A3E27E1","rank":"normal"}],"P5":[{"mainsnak":{"snaktype":"value","property":"P5","hash":"44d911672e4715d180bd3ef9412be3a182fda4fa","datavalue":{"value":{"entity-type":"item","numeric-id":67,"id":"Q67"},"type":"wikibase-entityid"},"datatype":"wikibase-item"},"type":"statement","id":"Q1680$267D7D0D-0130-4C4C-92DF-B65EAAA3D17F","rank":"normal"}]},"sitelinks":{}}}}