Department of Mathematics, University of the Punjab, Lahore, Pakistan.
Department of Mathematics, University of Peshawar, Peshawar, Pakistan.
PLoS One. 2021 Jan 22;16(1):e0244027. doi: 10.1371/journal.pone.0244027. eCollection 2021.
The approximate solution of KdV-type partial differential equations of order seven is presented. The algorithm based on one-dimensional Haar wavelet collocation method is adapted for this purpose. One-dimensional Haar wavelet collocation method is verified on Lax equation, Sawada-Kotera-Ito equation and Kaup-Kuperschmidt equation of order seven. The approximated results are displayed by means of tables (consisting point wise errors and maximum absolute errors) to measure the accuracy and proficiency of the scheme in a few number of grid points. Moreover, the approximate solutions and exact solutions are compared graphically, that represent a close match between the two solutions and confirm the adequate behavior of the proposed method.
给出了一类七阶 KdV 型偏微分方程的近似解。为此目的，采用了基于一维 Haar 小波配置法的算法。一维 Haar 小波配置法在 Lax 方程、Sawada-Kotera-Ito 方程和 Kaup-Kuperschmidt 方程的七阶方程上进行了验证。通过表格（包含逐点误差和最大绝对误差）显示逼近结果，以在少量网格点上测量方案的准确性和熟练度。此外，还通过图形比较了近似解和精确解，两者之间的吻合度较好，验证了所提出方法的有效性。
