public double Solve(Settings settings, List <double> taoValues, List <double> sigmaValues, double x, double y)
{
double result = 0;
var firstMathExpression = new MathExpression($"ln((sqrt({Math.Pow(y, 2)}+({x}-t)^2))^(0-1))");
var secondMathExpression = new MathExpression($"a*ln((sqrt(({x}-a*cos(t))^2+({y}-a*sin(t))^2))^(0-1))");
for (int j = 0; j < settings.PartitionsOnCrack; j++)
{
result += GaussMethodForIntegrals.CalculateWithAccuracy(settings.PartitionPoints[j], settings.PartitionPoints[j + 1], firstMathExpression, Constants.Epsilon, new Var("t", 0), new Var("s", settings.ColocationPoints[j])) * taoValues[j];
}
for (int j = 0; j < settings.PartitionsOnBound; j++)
{
var partitionIndex = j + settings.PartitionsOnCrack + 1;
result += settings.Radius.Value * GaussMethodForIntegrals.CalculateWithAccuracy(settings.PartitionPoints[partitionIndex], settings.PartitionPoints[partitionIndex + 1], secondMathExpression, Constants.Epsilon, new Var("t", 0), new Var("s", settings.ColocationPoints[j + settings.PartitionsOnCrack]), new Var("a", settings.Radius.Value)) * sigmaValues[j];
}
return(1 / (2 * Math.PI) * result);
}
private Dictionary <EquationsEnum, Func <Settings, int, int, double> > GetMatrixAInits()
{
var result = new Dictionary <EquationsEnum, Func <Settings, int, int, double> >();
result.Add(EquationsEnum.Equation_3_2, (settings, i, j) =>
{
j++;
if (settings.PartitionPoints[j - 1] > settings.ColocationPoints[i])
{
return(-((settings.PartitionPoints[j] - settings.ColocationPoints[i]) * Math.Log(settings.PartitionPoints[j] - settings.ColocationPoints[i]) - (settings.PartitionPoints[j - 1] - settings.ColocationPoints[i]) * Math.Log(settings.PartitionPoints[j - 1] - settings.ColocationPoints[i]) - (settings.PartitionPoints[j] - settings.PartitionPoints[j - 1])));
}
else
{
if (settings.PartitionPoints[j] < settings.ColocationPoints[i])
{
return(-(-(-settings.PartitionPoints[j] + settings.ColocationPoints[i]) * Math.Log(-settings.PartitionPoints[j] + settings.ColocationPoints[i]) + (-settings.PartitionPoints[j - 1] + settings.ColocationPoints[i]) * Math.Log(-settings.PartitionPoints[j - 1] + settings.ColocationPoints[i]) - (settings.PartitionPoints[j] - settings.PartitionPoints[j - 1])));
}
else
{
return(-((-settings.PartitionPoints[j - 1] + settings.ColocationPoints[i]) * Math.Log(-settings.PartitionPoints[j - 1] + settings.ColocationPoints[i]) + (settings.PartitionPoints[j] - settings.ColocationPoints[i]) * Math.Log(settings.PartitionPoints[j] - settings.ColocationPoints[i]) - (settings.PartitionPoints[j] - settings.PartitionPoints[j - 1])));
}
}
});
result.Add(EquationsEnum.Equation_3_3, (settings, i, j) =>
{
j++;
if (i == (j - 1))
{
return(2 * FredholmEquationFirstOrder.Calculate_Aij(settings.PartitionPoints, settings.ColocationPoints, i, j) - Math.Log(settings.Radius.Value) *
Math.Abs(settings.IntervalOfIntegration.Item2 - settings.IntervalOfIntegration.Item1) / settings.AmountOfPartitions +
GaussMethodForIntegrals.CalculateWithAccuracy(settings.PartitionPoints[j - 1], settings.PartitionPoints[j],
new MathExpression($"{settings.Radius.Value}*ln(1/({settings.FunctionDistance}))-ln(1/({settings.Radius.Value}*abs(t-{settings.ColocationPoints[i]})))"),
Constants.Epsilon, new Var(settings.Variables[0], 0), new Var(settings.Variables[1], settings.ColocationPoints[i]), new Var(settings.Variables[2], settings.Radius.Value)));
}
else
{
return(GaussMethodForIntegrals.CalculateWithAccuracy(settings.PartitionPoints[j - 1], settings.PartitionPoints[j],
new MathExpression($"{settings.Radius.Value}*ln(1/({settings.FunctionDistance}))"),
Constants.Epsilon, new Var(settings.Variables[0], 0), new Var(settings.Variables[1], settings.ColocationPoints[i]), new Var(settings.Variables[2], settings.Radius.Value)));
}
});
result.Add(EquationsEnum.Equation_3_4, (settings, i, j) =>
{
j++;
return(GaussMethodForIntegrals.CalculateWithAccuracy(settings.PartitionPoints[j - 1], settings.PartitionPoints[j],
new MathExpression($"ln(1/({settings.FunctionDistance}))*({settings.FunctionYakobian})"), Constants.Epsilon,
new Var(settings.Variables[0], 0), new Var(settings.Variables[1], settings.ColocationPoints[i]), new Var(settings.Variables[2], settings.Radius.Value)));
});
result.Add(EquationsEnum.Equation_3_5, (settings, i, j) =>
{
j++;
return(GaussMethodForIntegrals.CalculateWithAccuracy(settings.PartitionPoints[j - 1], settings.PartitionPoints[j],
new MathExpression($"ln(1/({settings.FunctionDistance}))*({settings.FunctionYakobian})"), Constants.Epsilon,
new Var(settings.Variables[0], 0), new Var(settings.Variables[1], settings.ColocationPoints[i]), new Var(settings.Variables[2], settings.Radius.Value)));
});
return(result);
}