You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Efficient solvers for time-dependent problems: a review of IMEX, LATIN, PARAEXP and PARAREAL algorithms for heat-type problems with potential use of approximate exponential integrators and reduced-order models 
Chapter Title:  Iterative methods: the LATIN approach 
1. Abstract of Cited Paper (BIB001):  This paper deals with the synergy between the LATIN multiscale method and what is called the Proper Generalized Decomposition (PGD) which is the key of its performances.

Literature Review:
A usual way to deal with nonlinear equations numerically is to use an iterative process within a fixed point algorithm. The LATIN (LArge Time INcremental) method pioneered by Ladevèze BIB001 and since then broadly used in computational structural Mechanics and material science (see BIB002 for a recent reference) solves time-dependent problems (linear or nonlinear) according to a two-step iterative process. To separate the difficulties, equations are partitioned into two groups: (i) a group of equations being local in space and time, possibly nonlinear (representing equilibrium equations for example); (ii) a group of linear equations, possibly global in the spatial variable. Then ad-hoc space-time approximations methods are used for the treatment of the global problem. Of course, space-time local equations can be solved in parallel, what makes the LATIN method efficient and suitable for today's HPC facilities. Let us emphasize that with LATIN, it is possible to solve hard nonlinear mechanics problems including thermodynamics irreversible problems (plasticity, friction as examples). As an llustration, let us describe the LATIN method on the (rather simple) nonlinear heat problem: and time) of the nonlinear problem (it can be an approximate solution obtained with a coarse solver for example); computeκ (0) = κ(u (0) ); 2. Iterate k, step 1 (global linear solution). Solve the linear problem with given initial and boundary conditions. 3. Iterate k, step 2 (local projection over the admissible manifold). Computẽ 4. Check convergence, k ← k + 1 if not and go to 2. The step 1 performs a global (linear) evolution of the solution whereas a pointwise nonlinear projection on the equilibrium conductivity coefficients is done in step 2. We have a natural convergence indicator in terms of distance between the frozen conductivitỹ κ and κ(u (k) ): In particular, if κ is Lipschitz continuous with Lipschitz constant L, then Remark that step 2 can be performed in parallel (in time). For better and faster convergence, one can imagine variant approaches using a relaxation approach: remark first that κ(u) is (formally) solution of the partial differential equation If κ is a strictly convex function for example, then the second term at the right hand side is negative. One may consider the approximate (augmented) problem where ε > 0 is a given relaxation time (assumed to be rather small). By this way, it is expected thatκ evolves much closer toward the value κ(u). One can then derive an iterative process with again two steps (linear solution + projection) as in the LATIN method.