A Numerical Method for Solving Boundary and Interior Layers Dominated Parabolic Problems with Discontinuous Convection Coefficient and Source Terms

Homotopy perturbation method for solving Caputo‐type fractional‐order Volterra‐Fredholm integro‐differential equations

“…We have provided sufficient conditions under which the present model problem has a unique solution. In addition, we have considered a semi-analytical approach that can be considered as an alternative to other approaches presented in several works, [9][10][11][12][13] based on the homotopy perturbation technique to approximate the solutions of the model equations.…”

“…Here, we are interested in obtaining the solution of fractional nonlinear integro-differential equations by using semi-analytical homotopy-based perturbation methods. [6][7][8] This approach makes the approximation simple for complicated models and can be considered as an alternative way to avoid the numerical discretizations provided in other works [9][10][11][12][13][14][15] for perturbation problems. Furthermore, the present method is not only an effective tool for approximation of the solution but it can also provide the exact solution of certain problems.…”

Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data

“…Lemma 11. When 2 ≤ , the singular components w l (x, t) and w r (x, t) of (18) to (19) satisfy the following bounds…”

“…10 The analysis for two-parameter problems mainly started by O'Malley, based on asymptotic expansion methods. 11 The numerical solution of these problems with smooth data [12][13][14][15] and nonsmooth data [16][17][18][19] are also considered in several journals and proceedings. Singularly perturbed parabolic problems are also considered for numerical analysis in Bansal et al and Munyakazi and Patidar.…”

Optimal Control Approach to Image Registration

“…Note: Algorithms have been produced lately to solve ODEs and PDEs by moving grids, the latest papers which show its effectiveness can be read in [19], [20], [21], [22], [23], [24], [32] and [33]. These references provide the technique that show the moving mesh algorithm and the discrete problem can be patched up to find the solution on adaptive mesh.…”