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Equation Solving by Iteration in Visual Basic

Learn how to solve equations iteratively using Visual Basic, including If-Then-Else statements, Newton-Raphson method, and Central Difference Method. Implement relative error calculation and iterate until specified tolerance or iteration limit is reached.

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Equation Solving by Iteration in Visual Basic

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  1. Using Visual Basic for Equation Solving by Iteration Introducing the Subroutine

  2. If, Then, Else Statement If(a < b) If a is less than b If(a = b) If a equals b If(a<>b) If a is not equal to b If(a<=b) If a is less than or equal to b If(a>=b) If a is greater than or equal to b If(a>b) Then If a is greater than b do these statements ElseIf (a=b) Then If a is equal to b do these statements Else a is neither greater do these statements than nor equal to b End if

  3. The Subroutine Public Function Functionname(arguments) Make calculations Call Subroutinename(b1, b2, b3, …, bn) Functionnname= some number End Function Public Sub Subroutinename(a1, a2, a3, …,an) Make calculations based on the arguments passed to subroutine End Sub

  4. How to Solve by Iteration

  5. Newton-Raphson Iteration

  6. Central Difference Method to Estimate the Derivative

  7. Calculating the Relative Error

  8. Continue to iterate until relerror is within some specified tolerance or until the number of iterations exceed some predetermined limit.

  9. Public tiny Public Function NewtonRaphson(arguments, xguess, tolerance, iter) x = xguess tiny = 1E-20 For i=1 to iter Call func(arguments,x, fx) Call deriv(arguments, x, dfdx, tiny) xnew = x – fx/dfdx relerror = abs(xnew - x)/(x + tiny) If(relerror < tolerance) Then Exit For Else x = xnew Endif Next i NewtonRaphson = xnew End Function Public Sub func(arguments, x, fx) Insert function here End Sub Public Sub deriv(arguments, x, dfdx) Call func(arguments, 1.01*(x + tiny), fhigh) Call func(arguments, 0.99*(x + tiny), flow) dfdx = (fhigh-flow)/(2*0.01*(x + tiny)) End Sub

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