Update Textarea from controller - asp.net-mvc-4

Question

I want to update textarea from controller after i found some result and page should not be reload. Is there any solution for this?
public class HomeController : Controller
{
public ActionResult Index()
{
return View();
}
public JsonResult SolveProblems(Problem[] array){
Solution sol=new Solution(array);
sol.OnSolutionFound+=sol_OnSolutionFound;
sol.OnTaskComplete+=sol_OnTaskComplete;
sol.Start();
return Json("Process started");
}
private void sol_OnSolutionFound(object sender, SolutionFoundEventArgs e)
{
// Here i want update textarea
}
private void sol_OnTaskComplete(object sender, SolutionCompletedEventArgs e)
{
// Here i want show process is finished
}
}
This is my html page. which contains some code and one textarea
..... some code....
<textarea class="form-control" id="ResultDisplay"></textarea>
<button type="button" id="btnSolve" class="btn btn-primary">Solve</button>
this is my javascript file
function GetProblems(){
...code...
return array;
}
$("#btnSolve").click(function () {
$.ajax({
type: "POST",
url: "/Home/SolveProblems",
contentType: "application/json; charset=utf-8",
data: JSON.stringify(GetProblems()),
dataType: "json",
success: function (response) {
},
error: function (response) {
alert("Unexpected error occurs!")
}
});
});

Answer 1

So, I have use SignalR and solve my problem as freedomn-m told me to do
I need to create a Hub by using i can send data when sol_OnSolutionFound is fired.
Here is my Hub
public class SolutionHub : Hub
{
public void SolutionFound(string Solution)
{
var hubContext = GlobalHost.ConnectionManager.GetHubContext<SolutionHub>();
hubContext.Clients.All.addNewMessageToPage(Solution);
}
}
Add section in Index.cshtml
#section scripts {
<!--Script references. -->
<!--The jQuery library is required and is referenced by default in _Layout.cshtml. -->
<!--Reference the SignalR library. -->
<script src="~/Scripts/jquery.signalR-2.2.2.min.js"></script>
<!--Reference the autogenerated SignalR hub script. -->
<script src="~/signalr/hubs"></script>
<!--SignalR script to update the chat page and send messages.-->
<script>
$(function () {
// Reference the auto-generated proxy for the hub.
var chat = $.connection.solutionHub;
// Create a function that the hub can call back to display messages.
chat.client.addNewMessageToPage = function (Solution) {
// Add the message to the page.
$("#ResultDisplay").append(Solution);
};
$.connection.hub.start().done(function () {
});
});
</script>
}
and finally need to call SolutionFound when sol_OnSolutionFound is fired.
private void sol_OnSolutionFound(object sender, SolutionFoundEventArgs e)
{
SolutionHub Hub=new SolutionHub();
Hub.SolutionFound(e.Solution);
}