public ParabolicExplicitFiniteDifference(
ParabolicBoundaryConditions conditions,
ParabolicEquationParams equation,
ParabolicFiniteDifferenceParams @params)
{
_params = @params;
_conditions = conditions;
_equation = equation;
_grid = new double[_params.SpaceStepCount + 1, _params.TimeStepCount + 1];
InitializeGrid();
}
public CrankNikolsonMethod(
ParabolicBoundaryConditions conditions,
ParabolicEquationParams equation,
FiniteDifferenceParams @params,
double weight = 0.5d)
{
_conditions = conditions;
_params = @params;
_equation = equation;
_weight = weight;
_grid = new double[_params.SpaceStepCount + 1, _params.TimeStepCount + 1];
InitializeGrid();
}
static void Main(string[] args)
{
var conditions = new ParabolicBoundaryConditions()
{
FirstConditionParameters = new[] { 1.0d, 1.0d },
SecondConditionParameters = new[] { 1.0d, 1.0d },
InitialCondition = (x, t) => Math.Sin(x),
FirstCondition = (x, t) => Math.Exp(-2 * t) * (Math.Sin(t) + Math.Cos(t)),
SecondCondition = (x, t) => - Math.Exp(-2 * t) * (Math.Sin(t) + Math.Cos(t))
};
var equation = new ParabolicEquationParams()
{
a = 1.0d,
b = 1.0d,
c = -1.0d,
f = (x, t) => 0
};
var @params = new ParabolicFiniteDifferenceParams()
{
SpaceBoundLeft = 0,
SpaceBoundRight = Math.PI,
TimeLimit = 1d,
SpaceStepCount = 20,
TimeStepCount = 400,
BoundaryApproximation = BoundaryApproximationType.SecondDegreeTwoPoints
};
var exp = new Expression();
var varList = new List <Variable>()
{
new Variable("x", 2),
new Variable("y", Math.E)
};
exp.FromString("(x^2 + 6 * e^y) / (3 - 8 / (2* y))", varList);
Console.WriteLine(exp.GetValue());
var method = new CrankNikolsonMethod(conditions, equation, @params);
var result = method.Solve();
var errors = method.FindError((x, t) => Math.Exp(-2 * t) * Math.Sin(x + t));
var maxError = FindMax(errors);
var median = FindMedian(errors);
Console.WriteLine($"Max error: {maxError}; median error: {median}");
Console.ReadKey();
}
