Representation of the exact solution for infinite system of linear equations

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].…”

A Solution of an Infinite System of Quadratic Equations in Reproducing Kernel Space

“…Reproducing kernel space possesses numerous good qualities, which have already turned out to be helpful solving various problems [1,2,4,5,8,9]. In this paper, on the one hand, we introduce a norm-preserving mapping ρ : 2 → W 1 2 such that the inner product in 2 is equal to the one defined in the reproducing kernel space W 1 2 .…”

A numerical approach for solving the high-order nonlinear singular Emden–Fowler type equations

“…This theory has been successfully applied to integral equations [14,15], partial differential equations [16], boundary value problems [17][18][19][20][21][22], fractional differential equations [23], and so on [24][25][26][27][28][29].…”