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  "body": "\n## Summary\n\nThe MacCormack method is an explicit second-order [[finite difference|X7HYEBA5SA]] scheme for hyperbolic [[conservation laws|8RA7AMWSAF]].\nIt makes a predictor step with forward differences and then a corrector step with backward differences.\nFor linear equations it coincides with the [[Lax–Wendroff method|YHZ9BCNDRZ]].\nFor nonlinear systems it is simpler to program, because it needs no Jacobian of the flux.\nIt was introduced for problems of computational fluid dynamics, such as compressible flow.\n\n## Explanations\n\n### L1 human\n\nThe method first makes a rough prediction of the next time level, looking one grid point ahead.\nIt then corrects this prediction, looking one grid point back, and averages the result with the old value.\nAlternating the two directions cancels the leading errors of each one-sided difference.\nThe result is second-order accurate, like a centred scheme, while each step uses only simple one-sided differences.\n",
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