private void SetBorderGrid(int k)
{
var d = _equation.d;
var a = _equation.a;
var b = _equation.b;
var c = _equation.c;
var h = (_params.SpaceBoundRight - _params.SpaceBoundLeft) / _params.SpaceStepCount;
var tau = _params.TimeLimit / _params.TimeStepCount;
var alpha = _conditions.FirstConditionParameters[0];
var betta = _conditions.FirstConditionParameters[1];
var gamma = _conditions.SecondConditionParameters[0];
var delta = _conditions.SecondConditionParameters[1];
var f0 = _conditions.FirstCondition(0, GetTimeCoordinate(k));
var fn = _conditions.SecondCondition(0, GetTimeCoordinate(k));
switch (_params.BoundaryApproximation)
{
case BoundaryApproximationType.FirstDegreeTwoPoints:
_grid[0, k] = -(alpha / h) / (betta - alpha / h) * _grid[1, k] +
f0 / (betta - alpha / h);
_grid[_params.SpaceStepCount, k] = (gamma / h) / (delta + gamma / h) * _grid[_params.SpaceStepCount - 1, k] +
fn / (delta + gamma / h);
break;
case BoundaryApproximationType.SecondDegreeThreePoints:
_grid[0, k] = 1 / (-3 * alpha / (2 * h) + betta) *
(f0 + alpha / (2 * h) * (_grid[2, k] - 4 * _grid[1, k]));
_grid[_params.SpaceStepCount, k] = 1 / (3 * gamma / (2 * h) + delta) *
(fn + gamma / (2 * h) * (4 * _grid[_params.SpaceStepCount - 1, k] - _grid[_params.SpaceStepCount - 2, k]));
break;
case BoundaryApproximationType.SecondDegreeTwoPoints:
var lam0 = (-2 * a / h - h / (tau * tau) - d * h / tau + c * h) / (2 * a - b * h);
var ro0 = (2 * a * _grid[1, k] / h
- h / (tau * tau) * (_grid[0, k - 2] - 2 * _grid[0, k - 1])
+ d * h * _grid[0, k - 1] / tau
+ _equation.f(0, GetTimeCoordinate(k)) * h)
/ (2 * a - b * h);
var lam1 = (2 * a / h + h / (tau * tau) + d * h / tau - c * h) / (2 * a + b * h);
var ro1 = (-2 * a * _grid[_params.SpaceStepCount - 1, k] / h
+ h / (tau * tau) * (_grid[_params.SpaceStepCount, k - 2] - 2 * _grid[_params.SpaceStepCount, k - 1])
- d * h * _grid[_params.SpaceStepCount, k - 1] / tau
+ _equation.f(GetSpaceCoordinate(_params.SpaceStepCount), GetTimeCoordinate(k)) * h)
/ (2 * a + b * h);
_grid[0, k] = (f0 - alpha * ro0) / (alpha * lam0 + betta);
_grid[_params.SpaceStepCount, k] = (fn - gamma * ro1) / (gamma * lam1 + delta);
break;
}
}
private double[] SetBorderGrid(int k, Matrix matrix)
{
var g = _equation.d;
var a = _equation.a;
var b = _equation.b;
var c = _equation.c;
var h = (_params.SpaceBoundRight - _params.SpaceBoundLeft) / _params.SpaceStepCount;
var tau = _params.TimeLimit / _params.TimeStepCount;
var alpha = _conditions.FirstConditionParameters[0];
var betta = _conditions.FirstConditionParameters[1];
var gamma = _conditions.SecondConditionParameters[0];
var delta = _conditions.SecondConditionParameters[1];
var f0 = _conditions.FirstCondition(0, GetTimeCoordinate(k));
var fn = _conditions.SecondCondition(0, GetTimeCoordinate(k));
var N = _params.SpaceStepCount;
var d = Enumerable
.Range(0, _params.SpaceStepCount + 1)
.Select(i =>
(2 * _grid[i, k - 1] - _grid[i, k - 2]) / (tau * tau)
+ g * _grid[i, k - 2] / (2 * tau)
+ _equation.f(GetSpaceCoordinate(i), GetTimeCoordinate(k)))
.ToArray();
switch (_params.BoundaryApproximation)
{
case BoundaryApproximationType.FirstDegreeTwoPoints:
d[0] = f0;
d[N] = fn;
matrix[0, 0] = betta - alpha / h;
matrix[0, 1] = alpha / h;
matrix[N, N - 1] = -gamma / h;
matrix[N, N] = delta + gamma / h;
break;
case BoundaryApproximationType.SecondDegreeThreePoints:
d[0] = f0;
d[N] = fn;
matrix[0, 0] = betta - 3 * alpha / (2 * h);
matrix[0, 1] = 2 * alpha / h;
matrix[0, 2] = (-alpha / (2 * h));
var sim = matrix[0, 2] / matrix[1, 2];
matrix[0, 0] -= sim * matrix[1, 0];
matrix[0, 1] -= sim * matrix[1, 1];
matrix[0, 2] -= sim * matrix[1, 2];
d[0] -= sim * d[1];
matrix[N, N - 2] = gamma / (2 * h);
matrix[N, N - 1] = -2 * gamma / h;
matrix[N, N] = delta + 3 * gamma / (2 * h);
sim = matrix[N, N - 2] / matrix[N - 1, N - 2];
matrix[N, N] -= sim * matrix[N - 1, N];
matrix[N, N - 1] -= sim * matrix[N - 1, N - 1];
matrix[N, N - 2] -= sim * matrix[N - 1, N - 2];
d[N] -= sim * d[N - 1];
break;
case BoundaryApproximationType.SecondDegreeTwoPoints:
var lam0 = (-2 * a / h - h / (tau * tau) - g * h / tau + c * h) / (2 * a - b * h);
var ro0 = (-h / (tau * tau) * (_grid[0, k - 2] - 2 * _grid[0, k - 1])
+ g * h * _grid[0, k - 1] / tau
+ _equation.f(0, GetTimeCoordinate(k)) * h)
/ (2 * a - b * h);
var lam1 = (2 * a / h + h / (tau * tau) + g * h / tau - c * h) / (2 * a + b * h);
var ro1 = (-2 * a * _grid[_params.SpaceStepCount - 1, k] / h
+ h / (tau * tau) * (_grid[_params.SpaceStepCount, k - 2] - 2 * _grid[_params.SpaceStepCount, k - 1])
- g * h * _grid[_params.SpaceStepCount, k - 1] / tau
+ _equation.f(GetSpaceCoordinate(_params.SpaceStepCount), GetTimeCoordinate(k)) * h)
/ (2 * a + b * h);
d[0] = f0 - alpha * ro0;
d[N] = fn - gamma * ro1;
matrix[0, 0] = alpha * lam0 + betta;
matrix[0, 1] = alpha * 2 * a / (h * (2 * a - b * h));
matrix[N, N - 1] = -gamma * 2 * a / (h * (2 * a + b * h));
matrix[N, N] = gamma * lam1 + delta;
break;
}
return(d);
}
