Package math.numericalmethods

Class NumericalIntegral

  • public class NumericalIntegral
extends java.lang.Object
    Objects of this class are able to perform numerical integration of a curve within a given range given that the function is continuous throughout that range.
    Author:
    JIBOYE Oluwagbemiro Olaoluwa

    • Field Detail

      • SYMBOLIC_INTEGRATION

        public static final int SYMBOLIC_INTEGRATION
        Use this to integrate using the integral symbol.
        See Also:
        Constant Field Values

      • FUNCTIONAL_INTEGRATION

        public static final int FUNCTIONAL_INTEGRATION
        Use this to integrate without using the integral symbol. Here, the intg() command containing the function and the bounds are specified.
        See Also:
        Constant Field Values

    • Constructor Detail

      • NumericalIntegral

        public NumericalIntegral​(double xLower,
                         double xUpper,
                         int iterations,
                         java.lang.String function)
        Parameters:
        xLower - The lower limit of x
        xUpper - The upper limit of x
        iterations - The number of iterations
        function - The name of a Function that has been defined before in the WorkSpace or an anonymous Function just specified.

      • NumericalIntegral

        public NumericalIntegral​(java.lang.String expression,
                         int chooseExpressionType)
        Parameters:
        expression - An expression containing information about the function whose integral is to be evaluated and the limits of integration. For example: function,2,4....means integrate function between horizontal coordinates 2 and 3. Direct examples would be: sin(x+1),3,4 cos(sinh(x-2/tan9x)),4,4.32 and so on.
        chooseExpressionType - Determines if the expression to integrate contains the integral symbol or not. F(x) = sin(x)/2x; intg(F(x),0,2,iterations)

    • Method Detail

      • setIterations

        public void setIterations​(int iterations)
        Set the number of iterations and ensure that it is even.
        Parameters:
        iterations -

      • getIterations

        public int getIterations()
        Returns:
        the number of iterations.

      • getFunction

        public Function getFunction()

      • setFunction

        public void setFunction​(Function function)

      • getxLower

        public double getxLower()

      • setxLower

        public void setxLower​(double xLower)

      • getxUpper

        public double getxUpper()

      • setxUpper

        public void setxUpper​(double xUpper)

      • findSimpsonIntegral

        public java.lang.String findSimpsonIntegral()
        Returns:
        the Simpson integral of the function Simpson's rule requires an even number of rectangular strips and so an odd number of ordinates(y-coordinates) The x distances must also be equal. h= (xUpper-xLower)/(2*m)

      • findSimpsonIntegral

        public java.lang.String findSimpsonIntegral​(double h)
        Returns:
        the Simpson integral of the function Simpson's rule requires an even number of rectangular strips and so an odd number of ordinates(y-coordinates) The x distances must also be equal. h= (xUpper-xLower)/(2*m)

      • findTrapezoidalIntegral

        public java.lang.String findTrapezoidalIntegral()
        Returns:
        the integral of the function using the trapezoidal rule.

      • findTrapezoidalIntegral

        public java.lang.String findTrapezoidalIntegral​(double h)
        Returns:
        the integral of the function using the trapezoidal rule.

      • findPolynomialIntegral

        public double findPolynomialIntegral()
        Returns:
        the integral of the function using the polynomial rule.

      • findHighRangeIntegralWithAdvancedPolynomial

        public double findHighRangeIntegralWithAdvancedPolynomial()
        Determines the integral in a given range by splitting the range into sub-ranges of width that are at most 0.1 units along x, and finding the polynomial curve for each sub-range.
        Returns:
        the integral of the function using the trapezoidal rule.

      • findHighRangeIntegral

        public double findHighRangeIntegral()
        Determines the integral in a given range by splitting the range into sub-ranges of width that are at most 0.1 units along x, and finding the polynomial curve for each sub-range.
        Returns:
        the integral of the function using the trapezoidal rule.

      • findGaussianQuadrature

        public double findGaussianQuadrature()
        Returns:
        The Gaussian Quadrature Version.

      • findAdvancedPolynomialIntegral

        public double findAdvancedPolynomialIntegral()
        Algorithm that combines a variant of the Simpson rule and the polynomial rule to produce higher accuracy integrals.

      • extractFunctionStringFromExpression

        public static void extractFunctionStringFromExpression​(java.util.List<java.lang.String> list)
        Analyzes the list and extracts the Function string from it.
        Parameters:
        list - The list to be analyzed. Direct examples would be: intg(@sin(x+1),4,7) intg(F,4,7) where F is a function that has been defined before in the workspace.. and so on. Simplifies the list to the form intg(funcName,x1,x2) or intg(funcName,x1,x2,iterations)

      • getVariable

        public java.lang.String getVariable()

      • main

        public static void main​(java.lang.String[] args)