Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

The values of <svg height="15.3203pt" id="M20" style="vertical-align:-5.70108pt" version="1.1" viewbox="0 -9.61922 29.6151 15.3203" width="29.6151pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,8.075,3.264)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="430" vert-adv-y="430"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,12.666,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,17.354,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z" id="g113-121"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="559" vert-adv-y="559"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,24.927,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg> and its derivatives.

International Journal of Partial Differential Equations

tab1

Table 1

Table 1: Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method 