Representation of the exact solution for a kind of nonlinear partial differential equation

Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods

“…Recently, using the RKHSM, Cui, Geng, Lin and Chen discussed singular linear two-point boundary value problem, singular nonlinear two-point periodic boundary value problem, nonlinear system of boundary value problems and nonlinear partial differential equations [40][41][42][43][44][45][46][47][48][49][50][51].…”

“…Reproducing kernel theory has important application in numerical analysis, differential equation, probability and statistics and so on [38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Recently, using the RKHSM, Cui, Geng, Lin and Chen discussed singular linear two-point boundary value problem, singular nonlinear two-point periodic boundary value problem, nonlinear system of boundary value problems and nonlinear partial differential equations [40][41][42][43][44][45][46][47][48][49][50][51].…”

Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations

“…Theorem 2 [30]. The Hilbert space W 1 2 0; 1 ½ is a complete reproducing kernel and its reproducing kernel function G x y ð Þ can be…”

“…The RKHS method was used by many authors to investigate several scientific applications side by side with their theory. The reader is kindly requested to go through [18][19][20][21][24][25][26][27][28][29][30][31][32][33][34][35][36] in order to know more details about RKHS method, including its history, its modification for use, its applications, its iterative property, and its characteristics.…”

A Computational Method for Nonlinear 2m‐th Order Boundary Value Problems

“…Recently, using the reproducing kernel space method, some authors discussed nonlinear operator equations, singular linear two-point boundary value problems, singular nonlinear two-point periodic boundary value problems, nonlinear systems of boundary value problems and nonlinear partial differential equations and so on [5,6,9,11,12,22].…”