English | Español

Try our Free Online Math Solver!

Online Math Solver

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.





SOLVE NONLINEAR EQUATION SYSTEM MAPLE SYMBOLIC
multiplying,dividing,adding,subtracting integers,solving radicals and square roots,Adding, subtracting, multiplying and dividing Integer worksheets,adding ,subtracting ,multiplying ,and dividing fractions,online calculator that solves complex trinomials,simple pre-algebra equations,solve my algebra problem with a calculator and fractions,convert decimal to fraction algebra worksheet,solving nonhomogeneous second order linear differential equation,adding and subtracting fractions with like denominators worksheet,HOW DO I DIVIDE A FRACTION BY A RADICAL FRACTION,example of pictures of plotting points on the graphing calculator,Like Terms Simplifying Algebraic Expressions Activities Lessons,error 13 dimension on a ti 86 graphing calculator solving linear equations,Pre-Algebra chapter 2 evaluate expressions, worksheet triangle expressions answers,solving nonlinear differential equations matlab,test for adding and subtracting negitive and positive numbers,help with the algebraic expression four times a number divided by three,solving quadratic equations by completing the square,multi root quadratic equation solver TI-83,greatest common factor for three number with variables,adding subtracting multiplying dividing integers,Maths worksheet for highest common factor & least common factor for year 7,math help containing equivalent fractions decimals and percentages,exponents Simplifying Multiplication Expressions Lesson Plan,order of fractions from least to greatest Glencoe,McGraw-Hill,quadratic equations square root property calculator,Solving Non Linear Simultaneous Equations,convert mixed number to decimal,solve my algebra problem with a calculator and fractions for free,simplify radical expressions calculator root,simplifying complex rational expressions solver,solving simultaneous equations with excel equation solver,examples of quadratic equations with fractional exponential,online factoring of complex quadratic equations with variables only,square roots and cube roots activity,worksheets on add subtract multiply divide fractions,solving basic algebra equations homework word problem,integer problems adding multiplying dividing subtract,slow steps balancing chemical equations with least common multiples,linear equation in two variables subject to linear constraint inequalities,solving second order linear difference equation,Quadratic Equation Calculator factor,Uniqueness of forcing terms in linear partial differential equations,solving addition and subtraction equations,finding the least common denominator for two rational expressions,solving cubed polynomials equations,What are sqaure root method of Quadratic Equations?,rules for adding variables in a square root,how use my Casio Calculator for solving linear equations,solving multiple variable polynomial equation,converting base 2 fraction to decimal fraction,quadratic equation extracting square root,find vertex of absolute value equations,slow steps for balancing chemical equations with least common multiples,value for variable expression radicals roots,solve nonlinear differential equation first order,slope solving by elimination online calculator,find suare root of real numbers,multiplying dividing adding subtracting fractions,fraction and decimal multiplying and dividing worksheets,prealgebra solving equations by multiplying and dividing worksheet,Algebra I help turning rational equations into linear equations,least common denominator calculator,solving quadratic equations completing the square,greatest common factor of two numbers is 871,adding subtracting multiplying and dividing integers,Like Terms Simplifying Algebraic Expressions Junior High,combining like terms in algebraic expressions worksheets,solving third order linear equations,techniques in getting the least common denominator in college algebra,dividing algebraic terms online free calculator,worksheet solving addition and subtraction equations,solving 2nd order differential equation,how do you divide and times add subtract integers worksheet,free help on a 4>3 solve the inequality. graph the solutions on a number line,how to solve multivariable algebra equation with fractions,how to solve exponential probability in TI-83 Plus calculator,adding and subtracting positive and negative integers free worksheets,solving second order nonhomogeneous differential equation,solving quadratic equations 3 variables,combining like terms powerpoint lesson,graphing linear equations on the coordinate plane powerpoint,Java method Convert Decimal Numbers to time,solving nonhomogeneous 2nd order differential equations,ti-83 plus solving systems of linear equations in three variables,Simplifying a sum of radical expressions calculator,solving quadratics by factoring powerpoints,math poems with the words, prime numbers, common multiples,common factors,multiply and divide rational expressions calculator,method to solve third order polynomials,simplifying exponents and square root calculator,solving second order nonlinear differential equations,convert decimal to fraction - formula,worksheets solving addition and subtraction equations,pre algebra adding and subtracting integers worksheet,solving partial differential equations by factoring,how to solve first order linear differential equations using laplace transform,free advanced algebra add subtract rational expressions,integers adding, subtracting, multiplying, dividing worksheet,how do you do the square root on the TI-83 plus graphic calculator?,simplified radical form square roots,worksheet on adding,subtracting,multiplying,dividing integers,Combining Like Terms pre-algebra worksheet,dividing fractions and mix numbers cheat problem solver,practice worksheets on adding, subtracting,multiplying,and dividing decimals. for 6th grade,fractions formula adding subtracting multiplying,how to solve second order linear nonhomogeneous differential equations,square odd integer multiple of 8 plus one triangle number,simplify dividing algebra expressions online calculator free,simplify square root of difference of two squares,adding subtracting dividing multiplying integers games,equation of the line solver ordered pairs,solving second order non-homogeneous differential equations,Multiplying rational expression fractions solver,solving absolute value and radical equations using restrictions,7th grade level variables and equations explanations Equations Substitution variables,factoring polynomials with a cubed term, tutorial,pre algebra distributive property prentice hall,adding, subtracting, multiplying, dividing integers,algebraic formula percentage number variable,convert decimal to square root fraction
Thank you for visiting our site! You landed on this page because you entered a search term similar to this: solve nonlinear equation system maple symbolic, here's the result:

MCS 471 --- Computer Problem 2 --- Fall 2004

Zeros of Nonlinear Equations:
Computational Comparisons


Programs with Computer Outputs are Due Monday 18 October 2004 in Class.

  • General Description:This computer problem involves finding zeros of nonlinear equationsusing the TWO of the solution systems:

    1. MATLAB* interactive numerical computational (matrix) system;
      AND
    2. Maple interactive symbolic/numeric computational system;

    Test your code using three test function examples given below, but your programs should be fairly general and NOT tailored to these examples.

    *A programming language system (like C or Fortran or their variants) may be substituted for the MATLAB system ifpreferred.


  • Output Requirements: For the TWO Above Systems, submit

    1. If MATLAB system, a MATLAB M-File program, and Command Windowoutput for the three test examples, well-documented
      (if substitute C/Fortran system, a single program with six procedures,two each for the three sets of test functions and derivatives, withoutput well-documented source code and output);

    2. If Maple system, a Maple worksheet of code for the three test examples and output, well-documented;


  • Documentation:Document your own code with a brief description of the problem,an important variables dictionary and headings for important programmingsteps (use programming language comment lines).


  • Newton Method Comparison:Implement the Newton's algorithm given in class with the stopping criteriagiven later.However, if iterations run out of the current COSI interval [a,b],then do three (3) bisection iterations to reduce the current COSI interval in size, then continue with Newton's method with the reduced COSI. Count all function evaluations used:

    1. If MATLAB programming, set "format long", implement Newton's methodand compare the answer to MATLAB's "[x_zero,f_zero] := fzero(f,x0);" if"f" is an inline defined function else use the function handle version "@f" if a m-file defined function "f" or else use the expression for thefunction enclosed in single quotes in place of the "f" argument of "fzero",where "x0" is the x-value argument of the "min(f(a),f(b))",while plotting each of the three functions on the initial interval "[a,b]".
      (If C/F programming substitute, use double precision (64 bits = 8 bytes, double in C or real*8 in Fortran) for Newton's and the comparison method. You may use C (CC or C++), Fortran (F77 or F90+) for this problem (else, see Prof. Hanson). Compare your Newton results to the Method of Bisection algorithm (also presented in class) using the number of iterations and the difference infinal zero position answers and the approximate value of the functionat that point.)

    2. If Maple programming, set "Digits = 16;", implement Newton's methodand compare the answer to Maple's "x_zero := fsolve(f(x)=0,x=a..b);" andthe value "f_zero := f(x_zero);", while plotting each of the three functionson the initial interval "[a,b]".


  • Newton Method Hybrid Absolute-Relative Stopping Criterion:

      abs(xnew-xold) + abs(fnew) < tolabs + tolrel*(abs(xold)+abs(fold))

      with absolute tolerance tolabs = 0.5e - 7 for all subroutines and tolrel = 10*deps where deps is the double precision machine epsilon (found forComputer Problem#1) for the relative tolerance scale.Iteration limit is kmax = 80 (i.e., abort current function case with message if k > kmax) and the Tolerance Lower Limit for Derivative, |f'(x)| > told, Divide Check is told = 0.5E - 10.


  • Three Good Test Examples:

    1. f1(x) = exp(-7.627*x) - x*exp(-4.759); on [0.2, 1.2];

    2. f2(x) = exp(4.947) - x*exp(4.854) + exp(2.252*x); on [0.0,2.0];

    3. f3(x) = 80.18*exp(-75.88*(x-0.5714)^2) - 77.09*exp(-75.97*(x-0.4903)^2);on [0.1,1.1].
    In each case use for the starting value the end point of the initialinterval that has the minimum function absolute value.


  • Additional and Special Output Requirements:

    1. Name of Your Computer System, Processor, MATLAB version (or substitute Compiler, and Compile Command Line) and Maple version;

    2. For each test example and Newton's method print a nicely labeled table of

      kfeval,     xold,     xnew,     abs(xnew-xold),     f(xnew),     f'(xold),    

      for all iterates displaying 5 significant digits. The item (f'(xold))is only used for the Newton's method.Give the starting value for both xnew andf(xnew) for the appropriate comparison method. Here, kfeval is total number of functionevaluations for current test function. The abs(xnew-xold)and f(xnew) items of the table should be printed ine-notation, because errors should almost always be in e-notation.


  • Helpful Information:

    1. Help on MATLAB:

      • Prof. Hanson's Help for MATLAB,

    2. Help on Maple Worksheets:

      • Beginner's Introduction to MapleV Release 5, or for more information see

      • Prof. Hanson's Help for Maple Symbolic Tools Archive

    3. Substitute C Caution: Do NOT forget to include math.h headers, andadd the compiler option -lm to the gcc (or any othercc variant) option list if needed (i.e., to remove errors because the compiler can not find some math functions). Also, C needs the powmath function, since it lacks an exponentiation symbol like "^".

    4. Substitute Fortran Caution: Do NOT forget that EXTERNAL statements are needed in Fortran, in all subprograms in which other subprograms are called with FUNCTIONarguments; the syntax is like EXTERNAL f1, f2, ..., fN and must comebefore any executable statements. Also, Fortran uses "**" for exponentiation instead of "^".


Web Source:

Email Comments or Questions (MCS 471 only, please) tohanson A T uic edu