All solutions are NaN in my Method of lines code. Please help.

Dear all,

I am trying to implement Method of lines (MOL) to solve my transient PDE. My solutions are all NaN except for the initial values.

'Index exceeds matrix dimensions.

Error in myFP (line 18)

dPdt(i)=((2*alpha^2.*x(i).*(1+h/2))+(h/2)*(2.*alpha.^2+beta)+(alpha.^2*x(i).^2)).*(y(i+1)/h^2)...

Error in solveFPE>@(t,y)myFP(t,y)

Error in odearguments (line 90)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in solveFPE (line 15)

[t,y]=ode45(@(t,y) myFP(t,y),tspan,y0);'

%% function defining the diff equation
function fval = myFP(~,y,x)
N=10; %number of intervals
P(1)=0;
P(2:N)=y;
P(N+1)=0;
h=0.1;

%paramters
alpha=0.25;
beta=0.75;
x=linspace(0,20,20);

%define dP/dt
dPdt=zeros(N+1,1);
for i=2:N
	dPdt(i)=(a^2*x(i).^(2)+2*a^(2)*x(i)+a^(2)*h+a^2*x(i)+b*h/2)*P(i+1)/h^(2)...
        -(a^2*x(i).^(2)+2*a^(2)*x(i))*P(i)/h^(2)...
    +(a^2*x(i).^(2)+2*a^(2)*x(i)-a^(2)*h-a^2*x(i)-b*h/2)*P(i-1)/h^(2);
end
 fval=dPdt(2:N);




%Initial conditions
N=10;
P0(1:N+1,1)=1;

y0=P0(2:N); 


tspan=linspace(0,20,20);
%solving the equation
[t,y]=ode45(@(t,y) myFP(t,y),tspan,y0);
plot(t,y)