PHP Form same page Submission message

I'm new to PHP and using the following code (which is working) but the page gets changed to another page, the website has different forms and I want the success message to appear on the form or any alert box format that doesn't effect the existing page. I need help with easy steps considering my beginning level.

MY HTML CODE:

<form action="order-mail.php" method="post" class="">
                <div class="row">
                    <div class="col-md-12">
                        <ul>
                            <li>
                                <i class="fa fa-user" aria-hidden="true"></i>
                                <input placeholder="Full Name *"  type="text" name="first_name" maxlength="50" size="30" required>
                            </li>
                        </ul>
                    </div>
                    <div class="col-md-6">
                        <ul>
                            <li>
                                <i class="fa fa-envelope" aria-hidden="true"></i>
                                <input placeholder="Email Address *"  type="text" name="email" maxlength="80" size="30">
                            </li>
                        </ul>
                    </div>
                    <div class="col-md-6">
                        <ul>
                            <li>
                                <i class="fa fa-phone" aria-hidden="true"></i>
                                <input placeholder="Phone No. *"  type="text" name="telephone" maxlength="30" size="30">
                            </li>
                        </ul>
                    </div>
                    <div class="col-md-12">
                        <ul>
                            <li>
                                <i class="fa fa-paper-plane-o" aria-hidden="true"></i>
                                <textarea  name="comments" placeholder="To help us understand better, enter a brief description about your project."></textarea>
                            </li>
                        </ul>
                    </div>
                    <div class="col-md-12">
                        <ul>
                            <li>
                                <input type="submit"  value="Submit">
                            </li>
                        </ul>
                    </div>
                </div>
            </form>

MY PHP CODE:

<?php
        if(isset($_POST['email'])) {

            // EDIT THE 2 LINES BELOW AS REQUIRED
          $email_to = "email@mydomain.com";
          $email_subject = "xyz Form Submissions";

          function died($error) {
                // your error code can go here
            echo "We are very sorry, but there were error(s) found with the form you submitted. ";
            echo "These errors appear below.<br /><br />";
            echo $error."<br /><br />";
            echo "Please go back and fix these errors.<br /><br />";
            die();
          }

            // validation expected data exists
          if(!isset($_POST['first_name']) ||
            !isset($_POST['email']) ||
            !isset($_POST['telephone']) ||
            !isset($_POST['comments'])) {
            died('We are sorry, but there appears to be a problem with the form you submitted.');       
        }

            $first_name = $_POST['first_name']; // required
            $email_from = $_POST['email']; // required
            $telephone = $_POST['telephone']; // not required
            $comments = $_POST['comments']; // required

            $error_message = "";
            $email_exp = '/^[A-Za-z0-9._%-]+@[A-Za-z0-9.-]+\.[A-Za-z]{2,4}$/';

            if(!preg_match($email_exp,$email_from)) {
              $error_message .= 'The Email Address you entered does not appear to be valid.<br />';
            }

            $string_exp = "/^[A-Za-z .'-]+$/";

            if(!preg_match($string_exp,$first_name)) {
              $error_message .= 'The First Name you entered does not appear to be valid.<br />';
            }

            if(strlen($comments) < 2) {
              $error_message .= 'The Comments you entered do not appear to be valid.<br />';
            }

            if(strlen($error_message) > 0) {
              died($error_message);
            }

            $email_message = "Form details below.\n\n";

            function clean_string($string) {
              $bad = array("content-type","bcc:","to:","cc:","href");
              return str_replace($bad,"",$string);
            }

            $email_message .= "First Name: ".clean_string($first_name)."\n";
            $email_message .= "Email: ".clean_string($email_from)."\n";
            $email_message .= "Telephone: ".clean_string($telephone)."\n";
            $email_message .= "Comments: ".clean_string($comments)."\n";

        // create email headers
            $headers = 'From: '.$email_from."\r\n".
            'Reply-To: '.$email_from."\r\n" .
            'X-Mailer: PHP/' . phpversion();
            @mail($email_to, $email_subject, $email_message, $headers);  

            ?>
            <!-- include your own success html here -->

            Thank you for the Submission

            <?php
          }
?>