The singular kernel coagulation equation with multifragmentation

A Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

On the Volterra Integral Equation with Weakly Singular Kernel

Wavelet‎-based numerical ‎method‎ ‎‎‎‎for solving fractional integro-differential equation with a weakly singular ‎kernel

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...

A simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three...

Self-similar Solutions to a Coagulation Equation with Multiplicative Kernel

Existence of self-similar solutions to the Oort-Hulst-Safronov coagulation equation with multiplicative coagulation kernel is established. These solutions are given by s(t)−τ ψτ (y/s(t)) for (t, y) ∈ (0, T )×(0,∞), where T is some arbitrary positive real number, s(t) = ((3−τ)(T − t))−1/(3−τ) and the parameter τ ranges in a given interval [τc, 3). In addition, the second moment of these self-sim...