This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
That's all the information needed. It includes two vital pieces of information:
1) you're getting an AbstractMethodError. This means that some piece of code is trying to call an abstract method that is not implemented. One cause could be an interface method that was added in a later version but not implemented yet.
2) javax.servlet.jsp.JspFactory.getJspApplicationContext(Ljavax/servlet/ServletContext;)Ljavax/servlet/jsp/JspApplicationContext indicates the method that is called. The class is javax.servlet.jsp.JspFactory, the method is public JspApplicationContext getJspApplicationContext(ServletContext).
I've checked the Javadocs on that method (just click on the JspFactory link), and it shows that this method has been available since "2.1". This means the JSP 2.1 specification. That surprises me a bit, because Tomcat 7 implements the JSP 2.2 specification (see http://tomcat.apache.org/tomcat-7.0-doc/). Do you perhaps have an older jsp-api.jar file on your class path?