TY - JOUR
T1 - Solution of Klein-Gordon Equation by a Method of Lines Using Reproducing Kernel Hilbert Space Method
AU - Patel , Kaushal
AU - Patel , Gautam
JO - Journal of Partial Differential Equations
VL - 3
SP - 251
EP - 262
PY - 2024
DA - 2024/08
SN - 37
DO - http://doi.org/10.4208/jpde.v37.n3.2
UR - https://global-sci.org/intro/article_detail/jpde/23341.html
KW - Method of Lines, reproducing kernel Hilbert space method, Klein-Gordon equation.
AB - <p style="text-align: justify;">This paper presents a method of lines solution based on the reproducing
kernel Hilbert space method to the nonlinear one-dimensional Klein-Gordon equation
that arises in many scientific fields areas. Our method uses discretization of the partial
derivatives of the space variable to get a system of ODEs in the time variable and then
solve the system of ODEs using reproducing kernel Hilbert space method. Consider
two examples to validate the proposed method. Compare the results with the exact
solution by calculating the error norms $L_2$ and $L_∞$ at various time levels. The results
show that the presented scheme is a systematic, effective and powerful technique for
the solution of Klein-Gordon equation.</p>