PSEM Approximations for Both Branches of Lambert <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2723999pt" id="M1" height="11.6718pt" version="1.1" viewBox="-0.0657574 -11.3994 16.908 11.6718" width="16.908pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-88" d="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z"/></g></svg> Function with Applications

<div><svg height="11.9316pt" id="M246" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 23.0755 11.9316" width="23.0755pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M185 344V453C137 433 92 421 41 413V386C100 378 104 375 104 310V106C104 41 97 35 33 30V0H268V30C190 35 185 41 185 107V283C206 340 240 371 267 371C282 371 296 364 310 351C316 344 325 343 336 348C357 357 369 378 369 399C369 424 345 451 310 451C262 451 219 397 187 344H185Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.465,3.132)"><path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.972,3.132)"><path d="M327 325C324 350 312 408 304 433C283 442 256 451 213 451C120 451 59 391 59 320C59 243 125 210 188 181C237 158 266 136 266 93C266 52 231 24 195 24C134 24 93 81 74 148L42 143C42 106 51 37 59 23C78 8 125 -12 177 -12C257 -12 345 35 345 127C345 198 292 234 216 264C171 283 131 305 131 348C131 387 156 416 195 416C243 416 277 378 297 317L327 325Z"></path></g></svg> for the different <svg height="8.8423pt" id="M247" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 3.66193 8.8423" width="3.66193pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z"></path></g></svg> trial functions for PSEM.</div>

Discrete Dynamics in Nature and Society

fig8

Figure 8

Figure 8: PSEM Approximations for Both Branches of Lambert <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2723999pt" id="M1" height="11.6718pt" version="1.1" viewBox="-0.0657574 -11.3994 16.908 11.6718" width="16.908pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-88" d="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z"/></g></svg> Function with Applications 

Discrete Dynamics in Nature and Society

PSEM Approximations for Both Branches of Lambert Function with Applications

Figure 8