Module: Mathpack::DifferentialEquations

Defined in:
lib/mathpack/differential_equations.rb

Class Method Summary collapse

Class Method Details

.generate_result(params, step, u) ⇒ Object 



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# File 'lib/mathpack/differential_equations.rb', line 66

def self.generate_result(params, step, u)
  result = { x: Mathpack::Approximation.generate_nodes(from: params[:from], to: params[:to], step: step) }
  u.each_index { |i| result[:"u#{i + 1}"] = u[i] }
  result
end

.runge_kutta_4(params = {}) ⇒ Object 



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# File 'lib/mathpack/differential_equations.rb', line 5

def self.runge_kutta_4(params = {})
  nodes = Mathpack::Approximation.generate_nodes(from: params[:from], to: params[:to], step: params[:step])
  y = Array.new(params[:system].length) { Array.new(nodes.length) }
  y.each_index do |i|
    y[i][0] = params[:y0][i]
  end
  fi0 = Array.new(y.length)
  fi1 = Array.new(y.length)
  fi2 = Array.new(y.length)
  fi3 = Array.new(y.length)
  for i in 0...nodes.length-1 do
    column = y.transpose[i]
    y_volna = Array.new(y.length)
    y.each_index do |j|
      fi0[j] = params[:system][j].call(nodes[i], *column)
    end
    y.each_index do |j|
      y_volna.each_index { |k| y_volna[k] = column[k] + 0.5 * params[:step] * fi0[k] }
      fi1[j] = params[:system][j].call(nodes[i] + 0.5 * params[:step], *y_volna)
    end
    y.each_index do |j|
      y_volna.each_index { |k| y_volna[k] = column[k] + 0.5 * params[:step] * fi1[k] }
      fi2[j] = params[:system][j].call(nodes[i] + 0.5 * params[:step], *y_volna)
    end
    y.each_index do |j|
      y_volna.each_index { |k| y_volna[k] = column[k] + params[:step] * fi2[k] }
      fi3[j] = params[:system][j].call(nodes[i + 1], *y_volna)
    end
    y.each_index do |j|
      y[j][i + 1] = y[j][i] + params[:step]/6.0 * (fi0[j] + 2.0 * fi1[j] + 2.0 * fi2[j] + fi3[j])
      y[j][i + 1] = y[j][i] + params[:step]/6.0 * (fi0[j] + 2.0 * fi1[j] + 2.0 * fi2[j] + fi3[j])
    end
  end
  y
end

.solve_cauchie_system(params = {}) ⇒ Object 



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# File 'lib/mathpack/differential_equations.rb', line 41

def self.solve_cauchie_system(params = {})
  params[:method] ||= :runge_kutta_4
  params[:m] = 2
  step = (params[:to] - params[:from]) / 2.0
  result = Mathpack::DifferentialEquations.send(params[:method], from: params[:from], to: params[:to], step: step, y0: params[:y0], system: params[:system], eps: params[:eps])
  u_next = Array.new(params[:system].length) { |i| result[i] }
  loop do
    u_prev = Array.new(u_next.length) { |i| u_next[i].dup }
    step /= 2.0
    result = Mathpack::DifferentialEquations.send(params[:method], from: params[:from], to: params[:to], step: step, y0: params[:y0], system: params[:system], eps: params[:eps])
    u_next.each_index do |i|
      u_next[i] = result[i]
    end
    is_finished = true
    u_next.each_index do |i|
      if Mathpack::IO.count_diff(u_next[i], u_prev[i]) / (2**params[:m] - 1) > params[:eps]
        is_finished = false
        break
      end
    end
    break if is_finished
  end
  generate_result(params, step, u_next)
end