382L-HW2/part2.html at master · fengivan/382L-HW2 · GitHub

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<html>
    <head>
        <meta charset = "utf-8">
        <title> HW2 Part 2</title>
        <script type="text/javascript" src="https://www.gstatic.com/charts/loader.js"></script>
        <style>
            table, th, td
            {
                border: 2px solid black;
            }
            .legend
            {
                font-weight:bold;
            }
            table
            {
                width: 25%;
                border-collapse: collapse;
            }
            #chart_div
            {
                width:1600px;
                height:1000px;
            }
        </style>
    </head>

    <body>
        <div id="problem">  </div>
    </body>

    <script>
        init();

        let deltax=parseFloat(document.getElementById("deltax").value);
        let deltat=parseFloat(document.getElementById("deltat").value);

        let grid=calculate();//calculates the explicit solution and stores it in grid
        let grid2=answer(); //gets the exact solution and stores it in grid2


        function init()
        {
            let linebreak = document.createElement("br");
            let prob = document.getElementById("problem");

            let probDescription = document.createElement("div");
            probDescription.innerHTML="Solution to differential equation using one point backward difference method for Ux and central difference method for Uxx";
            prob.appendChild(probDescription);
            prob.appendChild(linebreak.cloneNode(true));

            let deltaxlabel=document.createElement("label");                //adding text desciriptions
            deltaxlabel.innerHTML="Delta X: ";
            let deltaxinput=document.createElement("input");
            deltaxinput.setAttribute("type", "text");
            deltaxinput.id="deltax";
            deltaxinput.value=.025;
            deltaxinput.readOnly=true;
            prob.appendChild(deltaxlabel);
            prob.appendChild(deltaxinput);
            prob.appendChild(linebreak.cloneNode(true));
            let deltatlabel=document.createElement("label");
            deltatlabel.innerHTML="Delta T: ";
            let deltatinput=document.createElement("input");
            deltatinput.id="deltat";
            deltatinput.setAttribute("type", "text");
            deltatinput.value=.85/2720;
            deltatinput.readOnly=true;
            prob.appendChild(deltatlabel);
            prob.appendChild(deltatinput);
            prob.appendChild(linebreak.cloneNode(true));

            let createBtn = document.createElement("button");                   //adding buttons and event listeners
            createBtn.innerHTML = "Show Grid";
            createBtn.addEventListener("click", fillTable);
            prob.appendChild(createBtn);

            let showResults = document.createElement("button");
            showResults.innerHTML = "Show Results at T=.85";
            showResults.addEventListener("click", fillResults);
            prob.appendChild(showResults);


            let graphBtn = document.createElement("button");
            graphBtn.innerHTML="Show Graph of U explicit and U exact at T=.85";
            graphBtn.addEventListener("click", showGraph);
            prob.appendChild(graphBtn);

            let graphBtn2 = document.createElement("button");
            graphBtn2.innerHTML="Show Graph of Error T=.85";
            graphBtn2.addEventListener("click", showError);
            prob.appendChild(graphBtn2);

            let clearBtn = document.createElement("button");
            clearBtn.innerHTML="Clear";
            clearBtn.addEventListener("click", clear);
            prob.appendChild(clearBtn);
        }

        function showError()            //draws a graph of the absolute error, Math.abs(explicit - exact) at T=.85
        {
            clear();
            let chartdiv=document.createElement("div");
            chartdiv.id="chart_div";
            let prob = document.getElementById("problem");
            prob.appendChild(chartdiv);
            google.charts.load('current', {'packages':['corechart']});
            google.charts.setOnLoadCallback(drawErrorChart);
        }
        function drawErrorChart()       //helper function
        {
            let values=[];
            values.push(["X", "Error"]);

            let maxError=0;
            let xHighError=-1;
            for(let i = 0; i<=400; i++)
                {

                    let error=Math.abs(grid[grid.length-1][i]-grid2[grid2.length-1][i])
                    if(Math.abs(error)>maxError)
                    {
                        maxError=error;
                        xHighError=i*deltax;
                    }
                    values.push([i*deltax, error]);
                }
            let errormsg= document.createElement("div");
            errormsg.innerHTML="The Maximum Error is "+maxError+", located at x= "+xHighError;
            errormsg.id="error";
            document.getElementById("problem").appendChild(errormsg);

            let data = google.visualization.arrayToDataTable(values);
            let options = {
            title: 'Error of Explicit Solution  at T=.85',
            legend: {position: 'bottom'},
            hAxis: {title: 'X'},
            vAxis: {title: 'Error'},
            };
            let chart = new google.visualization.LineChart(document.getElementById("chart_div"));
            chart.draw(data, options);
        }

        function showGraph()            //draws a graph of the explicit and exact solutions at T=.85
        {
            clear();
            let chartdiv=document.createElement("div");
            chartdiv.id="chart_div";
            let prob = document.getElementById("problem");
            prob.appendChild(chartdiv);
            google.charts.load('current', {'packages':['corechart']});
            google.charts.setOnLoadCallback(drawChart);
        }

        function drawChart()            //helper function
        {
            let values=[];
            values.push(["X", "U calculated", "U exact"]);

            for(let i = 0; i<=400; i++)
                values.push([i*deltax, grid[grid.length-1][i], grid2[grid2.length-1][i]]);

            let data = google.visualization.arrayToDataTable(values);
            let options = {
            title: 'Explicit and Exact Solutions to U at T=.85',
            legend: {position: 'bottom'},
            hAxis: {title: 'X'},
            vAxis: {title: 'U'},
            };
            let chart = new google.visualization.LineChart(document.getElementById("chart_div"));
            chart.draw(data, options);
        }

        function clear()                //clears everything
        {
            if(document.getElementById("table"))
                document.getElementById("table").remove();
            if(document.getElementById("chart_div"))
                document.getElementById("chart_div").remove();
            if(document.getElementById("error"))
                document.getElementById("error").remove();
        }


        function answer()               // returns the exact solution
        {
            let grid2 = []
            for(let n=0; n<=2720; n++)    //time nodes
            {
                let b=[]
                for(let i=0; i<=400; i++)   //x
                {
                    b.push(Math.exp(n*deltat-i*deltax));
                }
                grid2.push(b);
            }
            return grid2;
        }

        function calculate()            //returns the explicit solution using 1 point backward difference for ux and 3 point central difference for uxx, the given boundry conditions, and a time step of .0003125 (or 2721 total nodes)
        {
            let grid = []                   //create the matrix
            for(let n=0; n<=2720; n++)    //time index, n*deltat=time
            {
                let b=[]
                for(let i=0; i<=400; i++)   //x index, i*deltax=x....
                {
                    if(n==0)
                    {
                        b.push(Math.exp(-i*deltax));            //t=0 boundry condition
                    }
                    else if (i ==0)
                    {
                        b.push(Math.exp(n*deltat));             //x = 0 boundry condition
                    }
                    else if (i!=400)                            //middle solution, calculates most of the nodes
                    {
                        let t1=(grid[n-1][i+1]-2*grid[n-1][i]+grid[n-1][i-1])/(deltax*deltax);      //see handwritten derivation
                        let t2=(grid[n-1][i+1]-grid[n-1][i-1])/(2*deltax);
                        let t3=grid[n-1][i];
                        b.push(grid[n-1][i]+deltat*(t1-t2-t3));
                    }
                    else if (i==400)                            //right boundry condition, x==10...
                    {
                        b.push(b[399]/(1+deltax));         //see derivation for this equation
                    }
                }
                grid.push(b);       //adds row to the matrix
            }
            return grid;
        }

        function fillResults()
        {
            clear();
            let prob = document.getElementById("problem");

            let table = document.createElement("table");
            table.id="table";

            let firstrow= document.createElement("tr");
            let xlabel=document.createElement("td");
            xlabel.innerHTML="X Value";
            xlabel.classList.add("legend");
            firstrow.appendChild(xlabel);

            let solutionlabel=document.createElement("td");
            solutionlabel.innerHTML="Numerical Solution";
            solutionlabel.classList.add("legend");
            firstrow.appendChild(solutionlabel);

            let exactsolutionlabel=document.createElement("td");
            exactsolutionlabel.innerHTML="Exact Solution";
            exactsolutionlabel.classList.add("legend");
            firstrow.appendChild(exactsolutionlabel);

            let errorlabel=document.createElement("td");
            errorlabel.innerHTML="Error";
            errorlabel.classList.add("legend");
            firstrow.appendChild(errorlabel);

            table.appendChild(firstrow);

            for(let i=0; i<grid[grid.length-1].length; i++)
            {
                let row= document.createElement("tr");
                let xval=document.createElement("td");
                xval.innerHTML=(i*deltax).toFixed(3);
                let nsolu=document.createElement("td");
                nsolu.innerHTML=(grid[grid.length-1][i]).toFixed(7);
                let exactsolu=document.createElement("td");
                exactsolu.innerHTML=(grid2[grid2.length-1][i]).toFixed(7);
                let error=document.createElement("td");
                error.innerHTML=(Math.abs(grid2[grid2.length-1][i]-grid[grid.length-1][i])).toFixed(10);
                row.appendChild(xval);
                row.appendChild(nsolu);
                row.appendChild(exactsolu);
                row.appendChild(error);
                table.appendChild(row);
            }


            prob.appendChild(table);
        }


        function fillTable()                                    //creates a table and fills table with the explicit solution
        {
            clear();
            let prob = document.getElementById("problem");

            let table = document.createElement("table");
            table.id="table";

            let firstrow= document.createElement("tr");
            let blank = document.createElement("td");
            blank.innerHTML=" ";
            firstrow.appendChild(blank);

            let xlabel=document.createElement("td");
            xlabel.innerHTML="X Value";
            xlabel.classList.add("legend");
            firstrow.appendChild(xlabel);

            let secondrow = document.createElement("tr");
            let timelabel=document.createElement("td");
            timelabel.innerHTML="Time";
            timelabel.classList.add("legend");
            secondrow.appendChild(timelabel);
            let nodelabel=document.createElement("td");
            nodelabel.innerHTML="Node";
            nodelabel.classList.add("legend");
            secondrow.appendChild(nodelabel);

            for(i=0; i<grid[0].length-1; i++)
            {
                let temp=document.createElement("td");
                let temp2=document.createElement("td");
                temp.innerHTML=(i*deltax).toFixed(3);
                temp2.innerHTML=i;
                temp.classList.add("legend");
                temp2.classList.add("legend");
                firstrow.appendChild(temp);
                secondrow.appendChild(temp2);
            }
            table.appendChild(firstrow);
            table.appendChild(secondrow);

            for(a=0; a<grid.length; a=a+10)
            {
                let row= document.createElement("tr");
                let time=document.createElement("td");
                time.innerHTML= (a*deltat).toFixed(3);
                time.classList.add("legend");
                let timenode=document.createElement("td");
                timenode.innerHTML=a;
                timenode.classList.add("legend");
                row.appendChild(time);
                row.appendChild(timenode);
                for(b=0; b<grid[a].length; b++)
                {
                    let xBox=document.createElement("td");
                    xBox.innerHTML=(grid[a][b]).toFixed(4);
                    row.appendChild(xBox);
                }
                table.appendChild(row);
            }
            prob.appendChild(table);
        }

    </script>
</html>