initial value problem can be solved by simulation whereas boundary value problem needs to be solved analytically
Not true as stated. There are lots of numerical boundary value problem solvers out there, one of better known is in Matlab PDE toolbox. The whole industry of Finite Element Method begs to disagree with your "needs to solved analytically" statement.
But you are right to say that
The boundary value, in contrast, means that you cannot find the next value in the sequence without finding the whole sequence.
Initial value problems (for ODE and PDE) can be solved by marching forward in time. For example, a simple solver for the diffusion equation would take three consecutive values of $u$ at time step $k$, say $u^{k}_{i-1}$, $u^k_i$, $u^k_{i+1}$, and calculate
$$u^{k+1}_i = bu^k_{i-1}+(1-2b)u^k_i+bu^k_{i+1}$$
where $0<b<1/2$ comes from the diffusion coefficient and the sizes of time step and space step.
Not so for boundary value problems. As you remarked, for ODE there is the shooting method, which attempts to solve a BVP by means of several IVPs. But the more systematic way, which works for both ODE and PDE, is to express the discrete form of PDE as a large (but sparse) linear system, and hit it with a specialized linear solver. For example, if I'm solving a boundary value problem for the Laplace equation, my linear system might consist of equations
$$u_{i\ j}=\frac14(u_{i-1\ j}+u_{i+1\ j} + u_{i\ j-1}+u_{i\ j+1})$$
which together with boundary conditions form a linear system with unique solution.
One practical consequence of this difference is that solution of initial value problems for PDE can be adapted to parallel computing easier than solution of boundary value problems.
The names themselves telling the meaning. Boundary conditions are those which depends on space while initial conditions are depends on time. So, in boundary condition space coordinate will be varied and in initial conditions time will be varied.
Best Answer
From here:
The two types of boundary conditions are used:
Essential or geometric boundary conditions which are imposed on the primary variable like displacements, and
Natural or force boundary conditions which are imposed on the secondary variable like forces and tractions.