Numerically solve a differential equation and return the solution.
NDSolveValue[eqns, expr, {x, xmin, xmax}]
NDSolveValue[eqns, expr, {x, xmin, xmax}, {y, ymin, ymax}]
NDSolveValue[eqns, expr, {x, y}∈ Ω]
NDSolveValue[eqns, u, {t, tmin, tmax}, {x, y}∈ Ω]
ysol = NDSolveValue[{y'[x] == y[x]Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}]
→ InterpolatingFunction[{{0., 30.}}, <>]ysol = NDSolveValue[{y''[x] + Sin[y[x]]y[x] == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 30}]
→ InterpolatingFunction[{{0., 30.}}, <>]Plot[Evaluate[NDSolveValue[{y''[x] + Sin[y[x]]y[x] == 0, y[0] == 1, y'[0] == 0}, {y[x], y'[x], y''[x]}, {x, 0, 30}]], {x, 0, 30}]
→ -Graphics-- AccuracyGoal — default Automatic
- Compiled — default Automatic
- DependentVariables — default Automatic
- EvaluationMonitor — default None
- InitialSeeding — default { }
- InterpolationOrder — default Automatic
- MaxStepFraction — default 1/10
- MaxSteps — default Automatic
- MaxStepSize — default Automatic
- Method — default Automatic
- NormFunction — default Automatic
- PrecisionGoal — default Automatic
- StartingStepSize — default Automatic
- StepMonitor — default None
- WorkingPrecision — default MachinePrecision