Programming a Differential Equation in C++: C++, Differential Equation

Programming a Differential Equation in C++

I have been tasked with the following assignment and would appreciate any assistance I can get.

"Develop a computer code for the solution of the problem that employs an Euler-Forward/Central Difference scheme, for 0 d t d 5, and graphically compare the exact and numerical solutions for x = 0.5."

Here is my incomplete rough draft so far. What I don't know how to do at all is the infinite summation. If anyone could assist I would be grateful. Thank you.

//Part 1
	double Pi = 3.14159265;
	double x = 0.5;
	double t = 0;
 
	//Part 2
	double n = 1;
	double e = 2.71828183;
	double rightSide;
	double rightSideTop;
 
	//Part 1
	double tempSum = 5 + x * t + 2/pow(Pi, 3);
 
	//Part 2
	rightSideTop = 1 - (pow(e,(-(Pi*Pi)*(n*n)*t)));
	rightSide = pow(-1,n) * ( rightSideTop / (n*n*n)) * sin(n*Pi*x);

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Here is my new try at this. Does this seem at all correct or am I way off?

//Defines
	double Pi = 3.14159265f;
	unsigned int infinite = 100000;
	double e = 2.71828183f;
 
	double x = 0.5f;
	double t = 0.0f;
 
	//Solution Array
	double Solution[1000] = {};
	ofstream myfile;
	myfile.open ("Results.txt");
 
	//Count of 1001 should be doing a loop for 0 <= t <= 5 at increments of 0.005
	for(int count = 0; count < 1001; count++)
	{	
		double summation = 0;
 
		//Simulating an Infinite summation?
		for(double n = 1.0f; n < infinite; n++)
		{	
			double rightSideTop = 1 - (pow(e,-(Pi*Pi) * (n*n) * t));
			double rightSide = pow((double)-1.0f,-n) * ( rightSideTop / (n*n*n)) * sin(n*Pi*x);
	
			summation += rightSide;
		}
 
		//Calculate the Result
		double h = 5 + (x * t) + (2.0f/(Pi*Pi*Pi) * summation);
 
		//Store the Calculated value at each interval
		Solution[count] = h;		
 
		//Progress 'Bar'
		cout << count << '\t';
		myfile << "t = " << t <<'\t' << "h = " << Solution[count] << '\n';
 
		t += 0.005f;
	}
 
	myfile.close();

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Programming a Differential Equation in C++

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C++

Differential Equation

Algorithms

Microsoft Visual C++.Net

Math & Science

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